diff --git a/papers/face_monochromatic_pairs/experiments/characterize_S_vertices.py b/papers/face_monochromatic_pairs/experiments/characterize_S_vertices.py index c316260..b15710d 100644 --- a/papers/face_monochromatic_pairs/experiments/characterize_S_vertices.py +++ b/papers/face_monochromatic_pairs/experiments/characterize_S_vertices.py @@ -28,7 +28,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_30_residual.py b/papers/face_monochromatic_pairs/experiments/check_30_residual.py index 40c962d..7c19367 100644 --- a/papers/face_monochromatic_pairs/experiments/check_30_residual.py +++ b/papers/face_monochromatic_pairs/experiments/check_30_residual.py @@ -29,7 +29,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_30_residual_v2.py b/papers/face_monochromatic_pairs/experiments/check_30_residual_v2.py index 4086549..fb6e71b 100644 --- a/papers/face_monochromatic_pairs/experiments/check_30_residual_v2.py +++ b/papers/face_monochromatic_pairs/experiments/check_30_residual_v2.py @@ -21,7 +21,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_S8_hit8_pG.py b/papers/face_monochromatic_pairs/experiments/check_S8_hit8_pG.py index 6967d37..9a057df 100644 --- a/papers/face_monochromatic_pairs/experiments/check_S8_hit8_pG.py +++ b/papers/face_monochromatic_pairs/experiments/check_S8_hit8_pG.py @@ -17,7 +17,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_S_adjacency.py b/papers/face_monochromatic_pairs/experiments/check_S_adjacency.py index e831774..4f2494c 100644 --- a/papers/face_monochromatic_pairs/experiments/check_S_adjacency.py +++ b/papers/face_monochromatic_pairs/experiments/check_S_adjacency.py @@ -21,7 +21,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_S_face_structure.py b/papers/face_monochromatic_pairs/experiments/check_S_face_structure.py index f5a4d74..0b7a502 100644 --- a/papers/face_monochromatic_pairs/experiments/check_S_face_structure.py +++ b/papers/face_monochromatic_pairs/experiments/check_S_face_structure.py @@ -23,7 +23,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_S_vs_pent_Fk.py b/papers/face_monochromatic_pairs/experiments/check_S_vs_pent_Fk.py index 0ddfe33..749e019 100644 --- a/papers/face_monochromatic_pairs/experiments/check_S_vs_pent_Fk.py +++ b/papers/face_monochromatic_pairs/experiments/check_S_vs_pent_Fk.py @@ -24,7 +24,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_bad_subcase_deciding_face.py b/papers/face_monochromatic_pairs/experiments/check_bad_subcase_deciding_face.py index 184fe64..07e0c40 100644 --- a/papers/face_monochromatic_pairs/experiments/check_bad_subcase_deciding_face.py +++ b/papers/face_monochromatic_pairs/experiments/check_bad_subcase_deciding_face.py @@ -28,7 +28,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_c28_no_chord_apex_kempe_constancy.py b/papers/face_monochromatic_pairs/experiments/check_c28_no_chord_apex_kempe_constancy.py index a642b59..55f858f 100644 --- a/papers/face_monochromatic_pairs/experiments/check_c28_no_chord_apex_kempe_constancy.py +++ b/papers/face_monochromatic_pairs/experiments/check_c28_no_chord_apex_kempe_constancy.py @@ -34,7 +34,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_conj_3_8_scaled.py b/papers/face_monochromatic_pairs/experiments/check_conj_final_scaled.py similarity index 99% rename from papers/face_monochromatic_pairs/experiments/check_conj_3_8_scaled.py rename to papers/face_monochromatic_pairs/experiments/check_conj_final_scaled.py index e0a9a15..86fcea3 100644 --- a/papers/face_monochromatic_pairs/experiments/check_conj_3_8_scaled.py +++ b/papers/face_monochromatic_pairs/experiments/check_conj_final_scaled.py @@ -16,7 +16,7 @@ the 4-edge-face criterion). Then we: partial(f_n). Aggregates per-n. -Run with: sage experiments/check_conj_3_8_scaled.py +Run with: sage experiments/check_conj_final_scaled.py """ from sage.all import Graph from sage.graphs.graph_generators import graphs diff --git a/papers/face_monochromatic_pairs/experiments/check_conj_on_holton_mckay.py b/papers/face_monochromatic_pairs/experiments/check_conj_on_holton_mckay.py index 52d8500..5277d6b 100644 --- a/papers/face_monochromatic_pairs/experiments/check_conj_on_holton_mckay.py +++ b/papers/face_monochromatic_pairs/experiments/check_conj_on_holton_mckay.py @@ -7,7 +7,7 @@ Each Holton-McKay graph is itself a cubic plane graph $G'$; its dual is a of a hypothetical minimal counterexample and apply the reduced-dual construction at each of its pentagonal faces. -Reuses the testing infrastructure from check_conj_3_8_scaled.py. +Reuses the testing infrastructure from check_conj_final_scaled.py. Run with: sage experiments/check_conj_on_holton_mckay.py """ @@ -19,7 +19,7 @@ from sage.all import Graph HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_constancy_obstruction.py b/papers/face_monochromatic_pairs/experiments/check_constancy_obstruction.py index 5920807..bb787fa 100644 --- a/papers/face_monochromatic_pairs/experiments/check_constancy_obstruction.py +++ b/papers/face_monochromatic_pairs/experiments/check_constancy_obstruction.py @@ -28,7 +28,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_cw_parity_prediction.py b/papers/face_monochromatic_pairs/experiments/check_cw_parity_prediction.py index 633ab06..7001206 100644 --- a/papers/face_monochromatic_pairs/experiments/check_cw_parity_prediction.py +++ b/papers/face_monochromatic_pairs/experiments/check_cw_parity_prediction.py @@ -31,7 +31,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_deciding_face.py b/papers/face_monochromatic_pairs/experiments/check_deciding_face.py index 47c78c0..f561570 100644 --- a/papers/face_monochromatic_pairs/experiments/check_deciding_face.py +++ b/papers/face_monochromatic_pairs/experiments/check_deciding_face.py @@ -26,7 +26,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_gprime_pentagon_always_works.py b/papers/face_monochromatic_pairs/experiments/check_gprime_pentagon_always_works.py index c8d2273..79dbe79 100644 --- a/papers/face_monochromatic_pairs/experiments/check_gprime_pentagon_always_works.py +++ b/papers/face_monochromatic_pairs/experiments/check_gprime_pentagon_always_works.py @@ -20,7 +20,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_heawood_local_side.py b/papers/face_monochromatic_pairs/experiments/check_heawood_local_side.py index c785fa2..fd3aa72 100644 --- a/papers/face_monochromatic_pairs/experiments/check_heawood_local_side.py +++ b/papers/face_monochromatic_pairs/experiments/check_heawood_local_side.py @@ -28,7 +28,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_heawood_on_kempe.py b/papers/face_monochromatic_pairs/experiments/check_heawood_on_kempe.py index fcfc86c..94838aa 100644 --- a/papers/face_monochromatic_pairs/experiments/check_heawood_on_kempe.py +++ b/papers/face_monochromatic_pairs/experiments/check_heawood_on_kempe.py @@ -22,7 +22,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_heawood_pair_mismatch.py b/papers/face_monochromatic_pairs/experiments/check_heawood_pair_mismatch.py index 5540fbe..e916630 100644 --- a/papers/face_monochromatic_pairs/experiments/check_heawood_pair_mismatch.py +++ b/papers/face_monochromatic_pairs/experiments/check_heawood_pair_mismatch.py @@ -23,7 +23,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_heawood_per_kempe_cycle.py b/papers/face_monochromatic_pairs/experiments/check_heawood_per_kempe_cycle.py index f6925f9..11ee242 100644 --- a/papers/face_monochromatic_pairs/experiments/check_heawood_per_kempe_cycle.py +++ b/papers/face_monochromatic_pairs/experiments/check_heawood_per_kempe_cycle.py @@ -18,7 +18,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_heawood_side_correlation.py b/papers/face_monochromatic_pairs/experiments/check_heawood_side_correlation.py index 5627a07..9c78280 100644 --- a/papers/face_monochromatic_pairs/experiments/check_heawood_side_correlation.py +++ b/papers/face_monochromatic_pairs/experiments/check_heawood_side_correlation.py @@ -24,7 +24,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_kb_kc_coverage.py b/papers/face_monochromatic_pairs/experiments/check_kb_kc_coverage.py index bfa2ec0..d10c90b 100644 --- a/papers/face_monochromatic_pairs/experiments/check_kb_kc_coverage.py +++ b/papers/face_monochromatic_pairs/experiments/check_kb_kc_coverage.py @@ -21,7 +21,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_kempe_intersection_and_alternation.py b/papers/face_monochromatic_pairs/experiments/check_kempe_intersection_and_alternation.py index 9a6a753..05b2167 100644 --- a/papers/face_monochromatic_pairs/experiments/check_kempe_intersection_and_alternation.py +++ b/papers/face_monochromatic_pairs/experiments/check_kempe_intersection_and_alternation.py @@ -33,7 +33,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_min_flip_structure.py b/papers/face_monochromatic_pairs/experiments/check_min_flip_structure.py index d76a368..4ff462b 100644 --- a/papers/face_monochromatic_pairs/experiments/check_min_flip_structure.py +++ b/papers/face_monochromatic_pairs/experiments/check_min_flip_structure.py @@ -21,7 +21,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_minority_location.py b/papers/face_monochromatic_pairs/experiments/check_minority_location.py index 3989e04..6540ee8 100644 --- a/papers/face_monochromatic_pairs/experiments/check_minority_location.py +++ b/papers/face_monochromatic_pairs/experiments/check_minority_location.py @@ -21,7 +21,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_shared_parity.py b/papers/face_monochromatic_pairs/experiments/check_shared_parity.py index 1a4aecd..a68f653 100644 --- a/papers/face_monochromatic_pairs/experiments/check_shared_parity.py +++ b/papers/face_monochromatic_pairs/experiments/check_shared_parity.py @@ -24,7 +24,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_shared_sequence_and_winding.py b/papers/face_monochromatic_pairs/experiments/check_shared_sequence_and_winding.py index b1c9b02..cb644b6 100644 --- a/papers/face_monochromatic_pairs/experiments/check_shared_sequence_and_winding.py +++ b/papers/face_monochromatic_pairs/experiments/check_shared_sequence_and_winding.py @@ -24,7 +24,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/check_subcase_iib.py b/papers/face_monochromatic_pairs/experiments/check_subcase_iib.py index 8ec9c36..6827a35 100644 --- a/papers/face_monochromatic_pairs/experiments/check_subcase_iib.py +++ b/papers/face_monochromatic_pairs/experiments/check_subcase_iib.py @@ -33,7 +33,7 @@ from sage.graphs.graph_generators import graphs HERE = os.path.dirname(os.path.abspath(__file__)) sys.path.insert(0, HERE) -from check_conj_3_8_scaled import ( +from check_conj_final_scaled import ( apply_reduction, proper_3_edge_colorings, matches_chord_apex_kempe, diff --git a/papers/face_monochromatic_pairs/experiments/test_n_21_to_24.py b/papers/face_monochromatic_pairs/experiments/test_n_21_to_24.py new file mode 100644 index 0000000..a86751e --- /dev/null +++ b/papers/face_monochromatic_pairs/experiments/test_n_21_to_24.py @@ -0,0 +1,252 @@ +"""Test Conjecture 5.1 (face-monochromatic-pair) on chord-apex+Kempe +colourings of reduced duals for n in [21, 24]. + +For each (G, v, i, φ) chord-apex+Kempe colouring, check: + (1) Is h_φ constant on V(K_b) ∪ V(K_c)? (= potential counterexample + to Conjecture 5.1) + (2) Is h_φ constant on V(K_b) alone? (= weaker condition, would + contradict Corollary 5.4) + (3) Does a deciding face exist (∂f ⊆ V(K_b) ∪ V(K_c) and |f| ≢ 0 + mod 3)? (= condition for the structural proof to apply) + +The known empirical result for n ≤ 20 is 0/142,812 for (1) and (2), +and 142,812/142,812 for (3). We extend to n = 21, 22, 23, 24. + +Results are written incrementally to results.jsonl in the cwd, so +that partial progress is preserved if the script is interrupted. + +The script also prints PROGRESS lines (= one per triangulation +processed, or every 10 minutes elapsed, whichever first) that can +be tailed for live monitoring. + +Run with: sage experiments/test_n_21_to_24.py +""" +import json +import os +import sys +import time +from pathlib import Path + +from sage.all import Graph +from sage.graphs.graph_generators import graphs + +HERE = os.path.dirname(os.path.abspath(__file__)) +sys.path.insert(0, HERE) + +from check_conj_final_scaled import ( + apply_reduction, + proper_3_edge_colorings, + matches_chord_apex_kempe, + kempe_cycle_set, + edge_idx, +) +from check_heawood_on_kempe import dual_of, heawood_numbers, vertices_of_kempe + + +RESULTS_FILE = Path(HERE) / '..' / 'test_n_21_to_24_results.jsonl' + + +def find_deciding_face(H, V_union): + """Return (face, |face|) for some deciding face, or None.""" + for f in H.faces(): + verts = {u for (u, v) in f} | {v for (u, v) in f} + if not verts.issubset(V_union): + continue + L = len(f) + if L % 3 != 0: + return f, L + return None + + +def test_one(D): + """For a given dual D, iterate reductions + chord-apex+Kempe + colourings, return a dict of counters.""" + D.is_planar(set_embedding=True) + n_col = 0 + n_const_kb = 0 + n_const_kb_kc_union = 0 + n_no_deciding = 0 + n_counterexamples = [] # save details of any counterexample + for face in D.faces(): + if len(face) != 5: continue + for i_red in range(5): + res = apply_reduction(D, face, i_red, 9999) + if res is None: continue + H = res['H']; named = res['named'] + H.is_planar(set_embedding=True) + edges, colorings = proper_3_edge_colorings(H) + cand = [c for c in colorings + if matches_chord_apex_kempe(edges, c, named)] + for col in cand: + n_col += 1 + try: + h = heawood_numbers(H, edges, col) + except RuntimeError: + continue + merged_idx = edge_idx(edges, named['merged']) + a = col[merged_idx] + bs = [c for c in range(3) if c != a] + kc_b = kempe_cycle_set(edges, col, merged_idx, (a, bs[0])) + kc_c = kempe_cycle_set(edges, col, merged_idx, (a, bs[1])) + V_b = vertices_of_kempe(edges, kc_b) + V_c = vertices_of_kempe(edges, kc_c) + V_union = V_b | V_c + # Check constancy + h_b_vals = {h[v] for v in V_b} + h_union_vals = {h[v] for v in V_union} + if len(h_b_vals) == 1: + n_const_kb += 1 + n_counterexamples.append({ + 'type': 'const_kb', + 'n_V_b': len(V_b), + }) + if len(h_union_vals) == 1: + n_const_kb_kc_union += 1 + n_counterexamples.append({ + 'type': 'const_union', + 'n_V_union': len(V_union), + }) + # Check deciding face + dec = find_deciding_face(H, V_union) + if dec is None: + n_no_deciding += 1 + n_counterexamples.append({ + 'type': 'no_deciding', + 'n_V_union': len(V_union), + }) + return n_col, n_const_kb, n_const_kb_kc_union, n_no_deciding, n_counterexamples + + +def write_result(record): + """Append a single JSONL record.""" + with open(RESULTS_FILE, 'a') as f: + f.write(json.dumps(record) + '\n') + f.flush() + + +def main(n_min=21, n_max=24, progress_every_seconds=600): + started_at = time.time() + # Clear / create the results file + print(f"Writing incremental results to {RESULTS_FILE}") + print(f"PROGRESS lines emitted every {progress_every_seconds}s " + f"(in addition to per-triangulation logs)") + sys.stdout.flush() + if RESULTS_FILE.exists(): + # Preserve old log under .bak; new run starts fresh + bak = RESULTS_FILE.with_suffix(RESULTS_FILE.suffix + '.bak') + RESULTS_FILE.rename(bak) + print(f"Previous results moved to {bak}") + RESULTS_FILE.touch() + + grand_col = 0 + grand_const_kb = 0 + grand_const_union = 0 + grand_no_deciding = 0 + + last_progress = time.time() + + for n in range(n_min, n_max + 1): + n_start = time.time() + print(f"\n=== n_G = {n} ===") + sys.stdout.flush() + try: + triangulations_iter = graphs.triangulations(n, minimum_degree=5) + except Exception as ex: + print(f"n={n}: cannot enumerate ({ex})") + continue + n_col_n = 0 + n_const_kb_n = 0 + n_const_union_n = 0 + n_no_deciding_n = 0 + tri_idx = 0 + for G in triangulations_iter: + G.is_planar(set_embedding=True) + D = dual_of(G) + tri_start = time.time() + nc, nck, ncu, nnd, examples = test_one(D) + tri_elapsed = time.time() - tri_start + n_col_n += nc + n_const_kb_n += nck + n_const_union_n += ncu + n_no_deciding_n += nnd + # Write per-triangulation record + record = { + 'n_G': n, 'tri_idx': tri_idx, + 'n_col': nc, + 'n_const_kb': nck, + 'n_const_kb_kc_union': ncu, + 'n_no_deciding': nnd, + 'tri_elapsed_s': round(tri_elapsed, 2), + 'wall_elapsed_s': round(time.time() - started_at, 2), + 'examples': examples, + } + write_result(record) + # Time-based progress line + now = time.time() + if now - last_progress >= progress_every_seconds: + wall_min = (now - started_at) / 60 + print(f"PROGRESS: wall {wall_min:.1f} min; " + f"n={n} tri {tri_idx+1} done ({tri_elapsed:.1f}s); " + f"running totals @n={n}: col={n_col_n}, " + f"const_kb={n_const_kb_n}, " + f"const_union={n_const_union_n}, " + f"no_dec={n_no_deciding_n}") + sys.stdout.flush() + last_progress = now + tri_idx += 1 + + n_elapsed = time.time() - n_start + # n-level summary record + summary = { + 'type': 'n_summary', + 'n_G': n, + 'n_tri': tri_idx, + 'n_col': n_col_n, + 'n_const_kb': n_const_kb_n, + 'n_const_kb_kc_union': n_const_union_n, + 'n_no_deciding': n_no_deciding_n, + 'n_elapsed_s': round(n_elapsed, 2), + 'wall_elapsed_s': round(time.time() - started_at, 2), + } + write_result(summary) + print(f"\nn={n}: {tri_idx} triangulations, {n_col_n} colourings " + f"[{n_elapsed:.0f}s]") + print(f" const_kb: {n_const_kb_n}") + print(f" const_kb_kc_union: {n_const_union_n}") + print(f" no_deciding_face: {n_no_deciding_n}") + sys.stdout.flush() + + grand_col += n_col_n + grand_const_kb += n_const_kb_n + grand_const_union += n_const_union_n + grand_no_deciding += n_no_deciding_n + + total_elapsed = time.time() - started_at + final = { + 'type': 'grand_summary', + 'n_min': n_min, 'n_max': n_max, + 'grand_col': grand_col, + 'grand_const_kb': grand_const_kb, + 'grand_const_kb_kc_union': grand_const_union, + 'grand_no_deciding': grand_no_deciding, + 'wall_elapsed_s': round(total_elapsed, 2), + } + write_result(final) + print("\n" + "=" * 70) + print(f"DONE: n in [{n_min}, {n_max}], " + f"{grand_col} chord-apex+Kempe colourings tested " + f"in {total_elapsed/60:.1f} min") + print(f" const_kb: {grand_const_kb}") + print(f" const_kb_kc_union: {grand_const_union}") + print(f" no_deciding_face: {grand_no_deciding}") + if (grand_const_kb == 0 and grand_const_union == 0 + and grand_no_deciding == 0): + print("✓ Conjecture 5.1 + Deciding-face conjecture EMPIRICALLY " + "EXTENDED to n_G ≤ {}".format(n_max)) + + +if __name__ == '__main__': + import sys + n_min = int(sys.argv[1]) if len(sys.argv) > 1 else 21 + n_max = int(sys.argv[2]) if len(sys.argv) > 2 else 24 + main(n_min=n_min, n_max=n_max) diff --git a/papers/face_monochromatic_pairs/paper.aux b/papers/face_monochromatic_pairs/paper.aux index 4405665..eea43c4 100644 --- a/papers/face_monochromatic_pairs/paper.aux +++ b/papers/face_monochromatic_pairs/paper.aux @@ -40,21 +40,50 @@ \newlabel{lem:both-kempe-constant}{{5.3}{11}} \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces The two cases in the proof of Lemma\nonbreakingspace 5.2\hbox {}. Vertices $v_0, v_1$ are consecutive on the $\{a, b\}$-Kempe cycle $K$, joined by an edge $e$, with the lemma's hypothesis $h_\varphi (v_0) = h_\varphi (v_1) = +1$ --- so both vertices share the clockwise colour order $(a, b, c)$. \emph {Left (Case\nonbreakingspace A):} when $\varphi (e) = a$, the colour-$b$ edge at $v_0$ lies south of $e$ (on $\partial F_R$) and the colour-$b$ edge at $v_1$ lies north of $e$ (on $\partial F_L$); the two would-be witness edges are on opposite faces, so no face of $\setbox \z@ \hbox {\mathsurround \z@ $\textstyle G$}\mathaccent "0362{G}'_{v,i}$ contains both. \emph {Right (Case\nonbreakingspace B):} when $\varphi (e) = b$, the colour-$a$ edges at $v_0, v_1$ are likewise on opposite sides of $e$. In either case the clause-$(3)$ arc of Conjecture\nonbreakingspace 5.1\hbox {} cannot be realised at $e$.}}{12}{}\protected@file@percent } \newlabel{fig:lemma-kempe-heawood}{{5}{12}} +\citation{Heawood1898} \newlabel{cor:single-cycle-non-constancy}{{5.4}{13}} -\newlabel{rem:heawood-empirical}{{5.5}{13}} -\newlabel{rem:conj-3-6-empirical}{{5.6}{13}} -\newlabel{conj:face-monochromatic-pair-strengthened}{{5.7}{14}} -\newlabel{rem:conj-3-8-empirical}{{5.8}{14}} +\newlabel{conj:no-two-constant-kempe-cycles}{{5.5}{13}} +\newlabel{rem:no-two-constant-kempe-cycles-counterexample}{{5.6}{13}} +\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Smallest counterexample to Conjecture\nonbreakingspace 5.5\hbox {}: a $C_{28}$ fullerene-style cubic plane graph (12 pentagons + 4 hexagons) with a proper $3$-edge-colouring on which $h_\varphi $ is simultaneously constant ($\equiv -1$) on the red/blue $12$-cycle and the red/green $12$-cycle, which share the colour-red edge $(0, 1)$. Light-shaded nodes are on $V(K_0) \cap V(K_1)$; medium-shaded on $V(K_0) \cup V(K_1) \setminus V(K_0) \cap V(K_1)$; grey on neither.}}{14}{}\protected@file@percent } +\newlabel{fig:no-two-constant-kempe-counterexample}{{6}{14}} +\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{A reduction of Conjecture 5.1\hbox {} via Heawood's face-sum identity}}{14}{}\protected@file@percent } +\newlabel{eq:heawood-face-sum}{{5.1}{14}} +\newlabel{conj:deciding-face}{{5.7}{14}} +\newlabel{thm:deciding-face-implies-conj-5-1}{{5.8}{14}} +\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{A partial structural proof of Conjecture\nonbreakingspace 5.7\hbox {}}}{15}{}\protected@file@percent } +\newlabel{def:flank-face}{{5.9}{15}} +\newlabel{lem:flank-length}{{5.10}{15}} +\newlabel{lem:flank-covering-base}{{5.11}{15}} +\newlabel{lem:flank-covering-hex}{{5.12}{16}} +\newlabel{thm:deciding-face-partial}{{5.13}{17}} +\newlabel{rem:n-i-6-flank-fails}{{5.14}{17}} +\newlabel{def:outer-face}{{5.15}{17}} +\newlabel{lem:outer-face-length}{{5.16}{17}} +\newlabel{lem:outer-face-covering-base}{{5.17}{17}} +\newlabel{thm:deciding-face-partial-extended}{{5.18}{18}} +\newlabel{rem:deciding-face-remaining-case}{{5.19}{18}} +\newlabel{conj:gprime-pentagon-fallback}{{5.20}{18}} +\newlabel{lem:gprime-pigeonhole}{{5.21}{18}} +\newlabel{rem:gprime-pigeonhole-stop}{{5.22}{18}} +\citation{AH77a} +\citation{AHK77} +\citation{RSST97} +\citation{Gonthier08} +\newlabel{rem:deciding-face-empirical}{{5.23}{20}} +\newlabel{rem:heawood-empirical}{{5.24}{20}} +\newlabel{rem:conj-3-6-empirical}{{5.25}{21}} +\newlabel{conj:face-monochromatic-pair-strengthened}{{5.26}{21}} +\newlabel{rem:conj-3-8-empirical}{{5.27}{22}} +\newlabel{rem:implication-4ct}{{5.28}{22}} \bibcite{Heawood1898}{1} \bibcite{AH77a}{2} \bibcite{AHK77}{3} \bibcite{RSST97}{4} \bibcite{Gonthier08}{5} \newlabel{tocindent-1}{0pt} -\newlabel{tocindent0}{12.7778pt} +\newlabel{tocindent0}{14.69437pt} 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[11] [12 <./fig_lemma_kempe_heawood.png>] -Overfull \hbox (45.67143pt too wide) in paragraph at lines 834--848 +Overfull \hbox (67.56044pt too wide) in paragraph at lines 850--860 +\OT1/cmr/m/n/10 and the ex-haus-tive search that found it is in \OT1/cmtt/m/n/1 +0 experiments/search[]min[]face5[]counterexample.py\OT1/cmr/m/n/10 . + [] + +LaTeX Font Info: Trying to load font information for OMS+cmtt on input line +872. +LaTeX Font Info: No file OMScmtt.fd. on input line 872. + +LaTeX Font Warning: Font shape `OMS/cmtt/m/n' undefined +(Font) using `OMS/cmsy/m/n' instead +(Font) for symbol `textbraceright' on input line 872. + + +File: figures/min-face-5-counterexample.png Graphic file (type png) + +Package pdftex.def Info: figures/min-face-5-counterexample.png used on input l +ine 882. +(pdftex.def) Requested size: 251.9989pt x 251.99138pt. + +LaTeX Warning: `h' float specifier changed to `ht'. + +[13] [14 <./figures/min-face-5-counterexample.png>] [15] +Overfull \hbox (15.85718pt too wide) detected at line 1071 +\OML/cmm/m/it/10 @F[] \OMS/cmsy/m/n/10 ^^R \OML/cmm/m/it/10 V\OT1/cmr/m/n/10 +(\OML/cmm/m/it/10 K[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 [ \OML/cmm/m/it/10 V\OT +1/cmr/m/n/10 (\OML/cmm/m/it/10 K[]\OT1/cmr/m/n/10 ) [] [] + [] + +[16] [17] +Overfull \hbox (133.90562pt too wide) in paragraph at lines 1248--1256 +\OT1/cmr/m/n/10 degree se-quence around $\OML/cmm/m/it/10 v$ \OT1/cmr/m/n/10 co +n-tains at least one degree-$5$ en-try (see \OT1/cmtt/m/n/10 experiments/check[ +]v[]neighbour[]degrees.py\OT1/cmr/m/n/10 ). + [] + + +Overfull \hbox (86.1788pt too wide) in paragraph at lines 1268--1278 +\OT1/cmr/bx/n/10 the chord-apex con-struc-tion). \OT1/cmr/m/n/10 Con-cretely (\ +OT1/cmtt/m/n/10 experiments/check[]bad[]subcase[]deciding[]face.py\OT1/cmr/m/n/ +10 ), + [] + + +Overfull \hbox (2.93471pt too wide) in paragraph at lines 1293--1295 +\OT1/cmr/bx/n/10 Lemma 5.21 \OT1/cmr/m/n/10 (Par-tial proof of Con-jec-ture 5.2 +0[] for small un-cov-ered set)\OT1/cmr/bx/n/10 . \OT1/cmr/m/it/10 If $\OMS/cmsy +/m/n/10 j\OML/cmm/m/it/10 V\OT1/cmr/m/n/10 ([]) \OMS/cmsy/m/n/10 n + [] + + +Overfull \hbox (4.00797pt too wide) in paragraph at lines 1311--1319 +\OT1/cmtt/m/n/10 experiments/check[]S[]adjacency.py\OT1/cmr/m/n/10 , \OT1/cmtt/ +m/n/10 experiments/check[]S[]face[]structure.py\OT1/cmr/m/n/10 ) + [] + +[18] +Overfull \hbox (12.19276pt too wide) in paragraph at lines 1323--1327 +\OML/cmm/m/it/10 K[]; K[]$ \OT1/cmr/m/n/10 are the ``other'' Kempe cy-cles in t +he $\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 c; c[]\OMS/cmsy/m/n/10 g$\OT1/cmr/m/n/10 + - and $\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 c; c[]\OMS/cmsy/m/n/10 g$\OT1/cmr/m/ +n/10 -decompositions. + [] + + +Overfull \hbox (19.83406pt too wide) in paragraph at lines 1365--1371 +\OT1/cmr/m/n/10 pentagon fall-back (Con-jec-ture 5.20[]) holds on $1[]314\OML/c +mm/m/it/10 =\OT1/cmr/m/n/10 1[]314 = 100%$ of chord-apex+Kempe + [] + + +Overfull \hbox (158.34045pt too wide) in paragraph at lines 1365--1371 +\OT1/cmr/m/n/10 colour-ings on which the par-tial struc-tural proof leaves a ga +p (\OT1/cmtt/m/n/10 experiments/check[]gprime[]pentagon[]always[]works.py\OT1/c +mr/m/n/10 ). + [] + +[19] +Overfull \hbox (68.54941pt too wide) in paragraph at lines 1451--1453 +\OT1/cmr/m/n/10 (Every length ap-pear-ing is $\OMS/cmsy/m/n/10 6^^Q \OT1/cmr/m/ +n/10 0([]3)$, as re-quired.) See \OT1/cmtt/m/n/10 experiments/check[]deciding[] +face.py\OT1/cmr/m/n/10 . + [] + + +Overfull \hbox (45.67143pt too wide) in paragraph at lines 1482--1496 [] [] -[13] -Underfull \hbox (badness 1648) in paragraph at lines 941--947 -\OT1/cmr/m/it/10 Remark \OT1/cmr/m/n/10 5.8\OT1/cmr/m/it/10 . \OT1/cmr/m/n/10 T -he strength-ened con-jec-ture was tested on the same chord- +[20] [21] +Underfull \hbox (badness 1112) in paragraph at lines 1589--1595 +\OT1/cmr/m/it/10 Remark \OT1/cmr/m/n/10 5.27\OT1/cmr/m/it/10 . \OT1/cmr/m/n/10 +The strength-ened con-jec-ture was tested on the same chord- [] +[22] [23] (./paper.aux) -Underfull \hbox (badness 1014) in paragraph at lines 941--947 -\OT1/cmr/m/n/10 apex+Kempe colour-ings as Re-mark 5.6[]; for each colour-ing we - sought any - [] +LaTeX Font Warning: Some font shapes were not available, defaults substituted. -[14] [15] (./paper.aux) ) + ) Here is how much of TeX's memory you used: - 3111 strings out of 478268 - 44673 string characters out of 5846347 - 350430 words of memory out of 5000000 - 21143 multiletter control sequences out of 15000+600000 - 478386 words of font info for 63 fonts, out of 8000000 for 9000 + 3174 strings out of 478268 + 45923 string characters out of 5846347 + 350679 words of memory out of 5000000 + 21190 multiletter control sequences out of 15000+600000 + 481842 words of font info for 75 fonts, out of 8000000 for 9000 1302 hyphenation exceptions out of 8191 - 69i,12n,76p,1047b,366s stack positions out of 10000i,1000n,20000p,200000b,200000s - - -Output written on paper.pdf (15 pages, 1086630 bytes). + 69i,13n,76p,1047b,404s stack positions out of 10000i,1000n,20000p,200000b,200000s +< +/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx9.pfb> + +< +/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi6.pfb> +Output written on paper.pdf (23 pages, 1328195 bytes). 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