From 8fde9494d8dafb5cfc07e758c756c9d16e95fee0 Mon Sep 17 00:00:00 2001 From: didericis Date: Fri, 22 May 2026 12:20:18 -0400 Subject: [PATCH] Add small-n ELG counting experiment (iso, rooted) count_elgs.py enumerates triangulation iso-classes and counts Even Level Graphs (G,v) per n: iso-classes (sources up to Aut) and flag-rooted (4E/|Aut| * s, an exact integer since Aut acts freely on flags). Co-Authored-By: Claude Opus 4.7 (1M context) --- .../experiments/count_elgs.py | 109 ++++++++++++++++++ .../paper.fdb_latexmk | 21 +++- .../paper.fls | 71 +++++++++++- .../paper.log | 2 +- .../paper.pdf | Bin 353656 -> 353656 bytes 5 files changed, 194 insertions(+), 9 deletions(-) create mode 100644 papers/level_resolutions_of_maximal_planar_graphs/experiments/count_elgs.py diff --git a/papers/level_resolutions_of_maximal_planar_graphs/experiments/count_elgs.py b/papers/level_resolutions_of_maximal_planar_graphs/experiments/count_elgs.py new file mode 100644 index 0000000..463ef39 --- /dev/null +++ b/papers/level_resolutions_of_maximal_planar_graphs/experiments/count_elgs.py @@ -0,0 +1,109 @@ +""" +Count Even Level Graphs (ELGs) for small n. + +An ELG is a pair (G, S) where G is a plane triangulation on n vertices, +S = {v} a single source vertex, and every level subgraph L_k (vertices at +BFS-distance k from v) is bipartite -- equivalently, every level cycle is +even (Definition: even-level-graph, sibling paper). + +We report per n: + - tri : # iso-classes of plane triangulations (maximal planar graphs) + - elg_iso : # iso-classes of ELG *pairs* (G,v), i.e. valid sources counted + up to Aut(G) + - elg_root : # flag-rooted ELGs = sum over iso-classes of 4E/|Aut(G)| * s(G), + E = 3n-6, s(G) = # valid sources. Aut(G) acts freely on the 4E + flags, so each term is an exact integer -- the small-integer, + automorphism-free count (the natural one for closed forms). +""" +import time +import networkx as nx +from networkx.algorithms.isomorphism import GraphMatcher + +from triangulation_gen import enumerate_all_triangulations + + +def is_even_level_graph(G, source): + """Every level subgraph L_k (BFS distance k from source) is bipartite, + equivalently every level cycle is even. Mirrors test_conjecture.py in + the even_level_graph_generators paper.""" + levels = {v: float("inf") for v in G.nodes()} + from collections import deque + dq = deque() + for s in source: + levels[s] = 0 + dq.append(s) + while dq: + v = dq.popleft() + for w in G[v]: + if levels[w] > levels[v] + 1: + levels[w] = levels[v] + 1 + dq.append(w) + if any(l == float("inf") for l in levels.values()): + return False, None # disconnected: source can't reach all vertices + for k in range(max(levels.values()) + 1): + L_k = G.subgraph([v for v in G.nodes() if levels[v] == k]) + if not nx.is_bipartite(L_k): + return False, None + return True, levels + + +def automorphisms(G): + """All automorphisms of G as node->node dict mappings.""" + return list(GraphMatcher(G, G).isomorphisms_iter()) + + +def valid_sources(G): + """Vertices v such that (G, {v}) is an ELG.""" + return [v for v in G.nodes() + if is_even_level_graph(G, frozenset({v}))[0]] + + +def source_orbits(G, sources, autos): + """Number of Aut(G)-orbits among the given source vertices.""" + src = set(sources) + seen, orbits = set(), 0 + for v in sources: + if v in seen: + continue + orbits += 1 + for a in autos: + seen.add(a[v]) + return orbits + + +def count_for_n(n): + tris = enumerate_all_triangulations(n) + flags = 4 * (3 * n - 6) # # flags of any n-vertex triangulation, E = 3n-6 + elg_iso = 0 + elg_root = 0 + n_elg_tris = 0 # triangulations admitting at least one ELG source + for G in tris: + srcs = valid_sources(G) + if not srcs: + continue + n_elg_tris += 1 + autos = automorphisms(G) + aut_size = len(autos) + elg_iso += source_orbits(G, srcs, autos) + # Aut acts freely on flags, so flags//aut_size is exact per class. + assert flags % aut_size == 0, (n, aut_size, flags) + elg_root += (flags // aut_size) * len(srcs) + return { + "tri": len(tris), + "tri_with_elg": n_elg_tris, + "elg_iso": elg_iso, + "elg_root": elg_root, + } + + +if __name__ == "__main__": + import sys + ns = [int(x) for x in sys.argv[1:]] or [4, 5, 6, 7, 8] + print(f"{'n':>3} {'tri':>6} {'tri+ELG':>8} {'elg_iso':>8} " + f"{'elg_root':>9} {'time':>6}") + for n in ns: + t0 = time.time() + r = count_for_n(n) + print(f"{n:>3} {r['tri']:>6} {r['tri_with_elg']:>8} " + f"{r['elg_iso']:>8} {r['elg_root']:>9} " + f"{time.time()-t0:>5.1f}s") diff --git a/papers/level_resolutions_of_maximal_planar_graphs/paper.fdb_latexmk b/papers/level_resolutions_of_maximal_planar_graphs/paper.fdb_latexmk index 65fd665..bb693de 100644 --- a/papers/level_resolutions_of_maximal_planar_graphs/paper.fdb_latexmk +++ b/papers/level_resolutions_of_maximal_planar_graphs/paper.fdb_latexmk @@ -1,6 +1,5 @@ # Fdb version 3 -["pdflatex"] 1779248022 "/Users/didericis/Code/math-research/papers/level_resolutions_of_maximal_planar_graphs/paper.tex" "paper.pdf" "paper" 1779248022 - "/Users/didericis/Code/math-research/papers/level_resolutions_of_maximal_planar_graphs/paper.tex" 1779248022 17051 e233978b7eec6e5db5857de6226f1fcb "" +["pdflatex"] 1779466804 "paper.tex" 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