From 41227c6a0f7fa8b902aed3aff289aa7557e7e09e Mon Sep 17 00:00:00 2001 From: didericis Date: Sun, 24 May 2026 15:04:15 -0400 Subject: [PATCH] papers: rename folders and retitle - Main paper: dual_decomposition_minimal_counterexamples/ -> face_monochromatic_pairs/. Title is now "Face-Monochromatic Pairs and the Four Colour Theorem". - Companion paper: dual_decomposition_iterated_reduction/ -> iterated_reduction_in_reduced_dual/. Title is now "An Iterated Reduction in the Reduced Dual". Its prose and bibliography cite the parent under the new title. - Update one absolute sys.path reference inside check_conj_face_kempe_n15.py that pointed at the old folder. Co-Authored-By: Claude Opus 4.7 --- .../experiments/check_all_distinct_exists.py | 0 .../experiments/check_conj_3_8_scaled.py | 0 .../experiments/check_conj_face_kempe.py | 0 .../experiments/check_conj_face_kempe_n15.py | 2 +- .../check_conj_face_kempe_scaled.py | 0 .../experiments/check_conj_on_holton_mckay.py | 0 .../check_constrained_feasibility.py | 0 .../experiments/check_dodecahedron_kempe.py | 0 .../experiments/check_kempe_class.py | 0 .../check_kempe_class_invariance.py | 0 .../experiments/check_kempe_class_monotone.py | 0 .../experiments/draw_chord_apex_proof.py | 0 .../draw_cubic_edge_contraction.py | 0 .../experiments/draw_lift_to_Gprime.py | 0 .../experiments/draw_reduced_dual_steps.py | 0 .../experiments/draw_step1_conj36.py | 0 .../draw_step1_conj36_recolored.py | 0 .../draw_thm_cubic_contraction_4face.py | 0 .../experiments/iterated_reduction.py | 0 .../experiments/reduced_dual.py | 0 .../search_conj_3_6_counterexample.py | 0 .../experiments/search_kempe_property.py | 0 .../fig_alg_step1_conj36.png | Bin .../fig_alg_step1_conj36_recolored.png | Bin .../fig_chord_apex_step1.png | Bin .../fig_chord_apex_step2.png | Bin .../fig_chord_apex_step3.png | Bin .../fig_cubic_edge_contraction.png | Bin .../fig_lift_to_Gprime.png | Bin .../fig_reduced_dual_step1.png | Bin .../fig_reduced_dual_step2.png | Bin .../fig_reduced_dual_step3.png | Bin .../fig_reduced_dual_step4.png | Bin .../fig_thm_cubic_contraction_4face.png | Bin .../paper.aux | 12 ++--- .../paper.fdb_latexmk | 0 .../paper.fls | 0 .../paper.log | 45 ++++++++++-------- .../paper.pdf | Bin 1017869 -> 1018017 bytes .../paper.tex | 2 +- .../experiments/draw_iterated_reduction.py | 0 .../draw_iterated_reduction_n14.py | 0 .../fig_alg_step0.png | Bin .../fig_alg_step1.png | Bin .../fig_alg_step2.png | Bin .../paper.aux | 0 .../paper.log | 6 +-- .../paper.pdf | Bin 387470 -> 385985 bytes .../paper.tex | 8 ++-- 49 files changed, 40 insertions(+), 35 deletions(-) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_all_distinct_exists.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_conj_3_8_scaled.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_conj_face_kempe.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_conj_face_kempe_n15.py (95%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_conj_face_kempe_scaled.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_conj_on_holton_mckay.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_constrained_feasibility.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_dodecahedron_kempe.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_kempe_class.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_kempe_class_invariance.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/check_kempe_class_monotone.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/draw_chord_apex_proof.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/draw_cubic_edge_contraction.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/draw_lift_to_Gprime.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/draw_reduced_dual_steps.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/draw_step1_conj36.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/draw_step1_conj36_recolored.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/draw_thm_cubic_contraction_4face.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/iterated_reduction.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/reduced_dual.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/search_conj_3_6_counterexample.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/experiments/search_kempe_property.py (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_alg_step1_conj36.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_alg_step1_conj36_recolored.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_chord_apex_step1.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_chord_apex_step2.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_chord_apex_step3.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_cubic_edge_contraction.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_lift_to_Gprime.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_reduced_dual_step1.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_reduced_dual_step2.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_reduced_dual_step3.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_reduced_dual_step4.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/fig_thm_cubic_contraction_4face.png (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/paper.aux (94%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/paper.fdb_latexmk (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/paper.fls (100%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/paper.log (92%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/paper.pdf (92%) rename papers/{dual_decomposition_minimal_counterexamples => face_monochromatic_pairs}/paper.tex (99%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/experiments/draw_iterated_reduction.py (100%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/experiments/draw_iterated_reduction_n14.py (100%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/fig_alg_step0.png (100%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/fig_alg_step1.png (100%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/fig_alg_step2.png (100%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/paper.aux (100%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/paper.log (98%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/paper.pdf (82%) rename papers/{dual_decomposition_iterated_reduction => iterated_reduction_in_reduced_dual}/paper.tex (98%) diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_all_distinct_exists.py b/papers/face_monochromatic_pairs/experiments/check_all_distinct_exists.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_all_distinct_exists.py rename to papers/face_monochromatic_pairs/experiments/check_all_distinct_exists.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_3_8_scaled.py b/papers/face_monochromatic_pairs/experiments/check_conj_3_8_scaled.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_3_8_scaled.py rename to papers/face_monochromatic_pairs/experiments/check_conj_3_8_scaled.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_face_kempe.py b/papers/face_monochromatic_pairs/experiments/check_conj_face_kempe.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_face_kempe.py rename to papers/face_monochromatic_pairs/experiments/check_conj_face_kempe.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_face_kempe_n15.py b/papers/face_monochromatic_pairs/experiments/check_conj_face_kempe_n15.py similarity index 95% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_face_kempe_n15.py rename to papers/face_monochromatic_pairs/experiments/check_conj_face_kempe_n15.py index defa88d..0ac5e5a 100644 --- a/papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_face_kempe_n15.py +++ b/papers/face_monochromatic_pairs/experiments/check_conj_face_kempe_n15.py @@ -4,7 +4,7 @@ from sage.graphs.graph_generators import graphs import sys # Reuse helpers from check_conj_face_kempe.py by importing -sys.path.insert(0, '/Users/didericis/Code/math-research/papers/dual_decomposition_minimal_counterexamples/experiments') +sys.path.insert(0, '/Users/didericis/Code/math-research/papers/face_monochromatic_pairs/experiments') from check_conj_face_kempe import ( dual_of, apply_reduction, proper_3_edge_colorings, kempe_cycle, edge_idx, matches_chord_apex_kempe, diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_face_kempe_scaled.py b/papers/face_monochromatic_pairs/experiments/check_conj_face_kempe_scaled.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_face_kempe_scaled.py rename to papers/face_monochromatic_pairs/experiments/check_conj_face_kempe_scaled.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_on_holton_mckay.py b/papers/face_monochromatic_pairs/experiments/check_conj_on_holton_mckay.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_on_holton_mckay.py rename to papers/face_monochromatic_pairs/experiments/check_conj_on_holton_mckay.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_constrained_feasibility.py b/papers/face_monochromatic_pairs/experiments/check_constrained_feasibility.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_constrained_feasibility.py rename to papers/face_monochromatic_pairs/experiments/check_constrained_feasibility.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_dodecahedron_kempe.py b/papers/face_monochromatic_pairs/experiments/check_dodecahedron_kempe.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_dodecahedron_kempe.py rename to papers/face_monochromatic_pairs/experiments/check_dodecahedron_kempe.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_kempe_class.py b/papers/face_monochromatic_pairs/experiments/check_kempe_class.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_kempe_class.py rename to papers/face_monochromatic_pairs/experiments/check_kempe_class.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_kempe_class_invariance.py b/papers/face_monochromatic_pairs/experiments/check_kempe_class_invariance.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_kempe_class_invariance.py rename to papers/face_monochromatic_pairs/experiments/check_kempe_class_invariance.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/check_kempe_class_monotone.py b/papers/face_monochromatic_pairs/experiments/check_kempe_class_monotone.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/check_kempe_class_monotone.py rename to papers/face_monochromatic_pairs/experiments/check_kempe_class_monotone.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/draw_chord_apex_proof.py b/papers/face_monochromatic_pairs/experiments/draw_chord_apex_proof.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/draw_chord_apex_proof.py rename to papers/face_monochromatic_pairs/experiments/draw_chord_apex_proof.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/draw_cubic_edge_contraction.py b/papers/face_monochromatic_pairs/experiments/draw_cubic_edge_contraction.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/draw_cubic_edge_contraction.py rename to papers/face_monochromatic_pairs/experiments/draw_cubic_edge_contraction.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/draw_lift_to_Gprime.py b/papers/face_monochromatic_pairs/experiments/draw_lift_to_Gprime.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/draw_lift_to_Gprime.py rename to papers/face_monochromatic_pairs/experiments/draw_lift_to_Gprime.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/draw_reduced_dual_steps.py b/papers/face_monochromatic_pairs/experiments/draw_reduced_dual_steps.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/draw_reduced_dual_steps.py rename to papers/face_monochromatic_pairs/experiments/draw_reduced_dual_steps.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/draw_step1_conj36.py b/papers/face_monochromatic_pairs/experiments/draw_step1_conj36.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/draw_step1_conj36.py rename to papers/face_monochromatic_pairs/experiments/draw_step1_conj36.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/draw_step1_conj36_recolored.py b/papers/face_monochromatic_pairs/experiments/draw_step1_conj36_recolored.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/draw_step1_conj36_recolored.py rename to papers/face_monochromatic_pairs/experiments/draw_step1_conj36_recolored.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/draw_thm_cubic_contraction_4face.py b/papers/face_monochromatic_pairs/experiments/draw_thm_cubic_contraction_4face.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/draw_thm_cubic_contraction_4face.py rename to papers/face_monochromatic_pairs/experiments/draw_thm_cubic_contraction_4face.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/iterated_reduction.py b/papers/face_monochromatic_pairs/experiments/iterated_reduction.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/iterated_reduction.py rename to papers/face_monochromatic_pairs/experiments/iterated_reduction.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/reduced_dual.py b/papers/face_monochromatic_pairs/experiments/reduced_dual.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/reduced_dual.py rename to papers/face_monochromatic_pairs/experiments/reduced_dual.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/search_conj_3_6_counterexample.py b/papers/face_monochromatic_pairs/experiments/search_conj_3_6_counterexample.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/search_conj_3_6_counterexample.py rename to papers/face_monochromatic_pairs/experiments/search_conj_3_6_counterexample.py diff --git a/papers/dual_decomposition_minimal_counterexamples/experiments/search_kempe_property.py b/papers/face_monochromatic_pairs/experiments/search_kempe_property.py similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/experiments/search_kempe_property.py rename to papers/face_monochromatic_pairs/experiments/search_kempe_property.py diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_alg_step1_conj36.png b/papers/face_monochromatic_pairs/fig_alg_step1_conj36.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_alg_step1_conj36.png rename to papers/face_monochromatic_pairs/fig_alg_step1_conj36.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_alg_step1_conj36_recolored.png b/papers/face_monochromatic_pairs/fig_alg_step1_conj36_recolored.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_alg_step1_conj36_recolored.png rename to papers/face_monochromatic_pairs/fig_alg_step1_conj36_recolored.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_chord_apex_step1.png b/papers/face_monochromatic_pairs/fig_chord_apex_step1.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_chord_apex_step1.png rename to papers/face_monochromatic_pairs/fig_chord_apex_step1.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_chord_apex_step2.png b/papers/face_monochromatic_pairs/fig_chord_apex_step2.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_chord_apex_step2.png rename to papers/face_monochromatic_pairs/fig_chord_apex_step2.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_chord_apex_step3.png b/papers/face_monochromatic_pairs/fig_chord_apex_step3.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_chord_apex_step3.png rename to papers/face_monochromatic_pairs/fig_chord_apex_step3.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_cubic_edge_contraction.png b/papers/face_monochromatic_pairs/fig_cubic_edge_contraction.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_cubic_edge_contraction.png rename to papers/face_monochromatic_pairs/fig_cubic_edge_contraction.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_lift_to_Gprime.png b/papers/face_monochromatic_pairs/fig_lift_to_Gprime.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_lift_to_Gprime.png rename to papers/face_monochromatic_pairs/fig_lift_to_Gprime.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_reduced_dual_step1.png b/papers/face_monochromatic_pairs/fig_reduced_dual_step1.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_reduced_dual_step1.png rename to papers/face_monochromatic_pairs/fig_reduced_dual_step1.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_reduced_dual_step2.png b/papers/face_monochromatic_pairs/fig_reduced_dual_step2.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_reduced_dual_step2.png rename to papers/face_monochromatic_pairs/fig_reduced_dual_step2.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_reduced_dual_step3.png b/papers/face_monochromatic_pairs/fig_reduced_dual_step3.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_reduced_dual_step3.png rename to papers/face_monochromatic_pairs/fig_reduced_dual_step3.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_reduced_dual_step4.png b/papers/face_monochromatic_pairs/fig_reduced_dual_step4.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_reduced_dual_step4.png rename to papers/face_monochromatic_pairs/fig_reduced_dual_step4.png diff --git a/papers/dual_decomposition_minimal_counterexamples/fig_thm_cubic_contraction_4face.png b/papers/face_monochromatic_pairs/fig_thm_cubic_contraction_4face.png similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/fig_thm_cubic_contraction_4face.png rename to papers/face_monochromatic_pairs/fig_thm_cubic_contraction_4face.png diff --git a/papers/dual_decomposition_minimal_counterexamples/paper.aux b/papers/face_monochromatic_pairs/paper.aux similarity index 94% rename from papers/dual_decomposition_minimal_counterexamples/paper.aux rename to papers/face_monochromatic_pairs/paper.aux index 3a68a03..3501d07 100644 --- a/papers/dual_decomposition_minimal_counterexamples/paper.aux +++ b/papers/face_monochromatic_pairs/paper.aux @@ -18,17 +18,17 @@ \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The four steps of Definition\nonbreakingspace 3.1\hbox {}, illustrated on $G' = $ the dodecahedron (dual of the icosahedron) with $F_v$ the inner pentagon and $i = 0$. Top left: delete the five boundary vertices of $F_v$, leaving five degree-$2$ vertices on a new face $F$. Top right: order them clockwise as $A_0,\dots ,A_4$. Bottom left: add $v_n$ joined to $A_0, A_1, A_2$. Bottom right: add the chord $A_3 A_4$, giving the cubic plane graph $\setbox \z@ \hbox {\mathsurround \z@ $\textstyle G$}\mathaccent "0362{G}'_{v,0}$.}}{4}{}\protected@file@percent } \newlabel{fig:reduced-dual-steps}{{1}{4}} \newlabel{def:edge-names}{{3.3}{4}} -\newlabel{lem:pentagonal-externals}{{3.4}{4}} -\newlabel{lem:chord-apex}{{3.6}{5}} -\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The proof of Lemma\nonbreakingspace 3.6\hbox {}, illustrated for $i = 0$ on $G' = $ the dodecahedron. Top: under the assumption $W \neq Y$, propriety at $v_n$ forces $W \in \{X, Z\}$. Bottom: in either case the lift to $G'$ has externals satisfying the hypothesis of Lemma\nonbreakingspace 3.4\hbox {}, which colours $\partial F_v$ to extend $\psi $ to a proper $3$-edge-colouring of $G'$.}}{6}{}\protected@file@percent } -\newlabel{fig:chord-apex-proof}{{2}{6}} +\newlabel{lem:pentagonal-externals}{{3.4}{5}} +\newlabel{lem:chord-apex}{{3.6}{6}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The proof of Lemma\nonbreakingspace 3.6\hbox {}, illustrated for $i = 0$ on $G' = $ the dodecahedron. Top: under the assumption $W \neq Y$, propriety at $v_n$ forces $W \in \{X, Z\}$. Bottom: in either case the lift to $G'$ has externals satisfying the hypothesis of Lemma\nonbreakingspace 3.4\hbox {}, which colours $\partial F_v$ to extend $\psi $ to a proper $3$-edge-colouring of $G'$.}}{7}{}\protected@file@percent } +\newlabel{fig:chord-apex-proof}{{2}{7}} \newlabel{lem:kempe-spike}{{3.7}{7}} \@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Edge suppression}}{8}{}\protected@file@percent } \newlabel{sec:edge-suppression}{{4}{8}} \newlabel{def:edge-suppression}{{4.1}{8}} -\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Edge suppression (Definition\nonbreakingspace 4.1\hbox {}). Left: a fragment of a cubic plane graph with the suppressed edge $e = uv$ highlighted in red. Middle: deleting $e$ leaves $u$ and $v$ of degree\nonbreakingspace $2$. Right: smoothing $u$ and $v$ replaces each pair of incident edges by a single new edge, removing $u, v$ and giving a cubic plane graph again.}}{8}{}\protected@file@percent } -\newlabel{fig:edge-suppression}{{3}{8}} \newlabel{thm:edge-suppression-4face}{{4.2}{8}} +\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Edge suppression (Definition\nonbreakingspace 4.1\hbox {}). Left: a fragment of a cubic plane graph with the suppressed edge $e = uv$ highlighted in red. Middle: deleting $e$ leaves $u$ and $v$ of degree\nonbreakingspace $2$. Right: smoothing $u$ and $v$ replaces each pair of incident edges by a single new edge, removing $u, v$ and giving a cubic plane graph again.}}{9}{}\protected@file@percent } +\newlabel{fig:edge-suppression}{{3}{9}} \@writefile{toc}{\contentsline {section}{\tocsection {}{5}{The face-monochromatic-pair conjecture and the Four Colour Theorem}}{9}{}\protected@file@percent } \newlabel{sec:toward-4ct}{{5}{9}} \newlabel{conj:face-monochromatic-pair-on-merged-kempe-cycle}{{5.1}{9}} diff --git a/papers/dual_decomposition_minimal_counterexamples/paper.fdb_latexmk b/papers/face_monochromatic_pairs/paper.fdb_latexmk similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/paper.fdb_latexmk rename to papers/face_monochromatic_pairs/paper.fdb_latexmk diff --git a/papers/dual_decomposition_minimal_counterexamples/paper.fls b/papers/face_monochromatic_pairs/paper.fls similarity index 100% rename from papers/dual_decomposition_minimal_counterexamples/paper.fls rename to papers/face_monochromatic_pairs/paper.fls diff --git a/papers/dual_decomposition_minimal_counterexamples/paper.log b/papers/face_monochromatic_pairs/paper.log similarity index 92% rename from papers/dual_decomposition_minimal_counterexamples/paper.log rename to papers/face_monochromatic_pairs/paper.log index 765488f..d46587d 100644 --- a/papers/dual_decomposition_minimal_counterexamples/paper.log +++ b/papers/face_monochromatic_pairs/paper.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 24 MAY 2026 14:42 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 24 MAY 2026 15:03 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -191,6 +191,9 @@ Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4 File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv e )) +Overfull \vbox (1.31958pt too high) has occurred while \output is active [] + + [1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] Overfull \hbox (41.917pt too wide) in paragraph at lines 233--235 @@ -199,42 +202,40 @@ d $\OML/cmm/m/it/10 F$ \OT1/cmr/m/n/10 as $\OML/cmm/m/it/10 A \OT1/cmr/m/n/10 = (\OML/cmm/m/it/10 A[]; A[]; A[]; A[]; A[]\OT1/cmr/m/n/10 )$. 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\section{Setup and background} \label{sec:background} -This paper is a follow-up to \emph{Dual Decomposition of Minimal -Counterexamples}~\cite{parent}, which introduced the reduced-dual +This paper is a follow-up to \emph{Face-Monochromatic Pairs and the Four +Colour Theorem}~\cite{parent}, which introduced the reduced-dual construction: given a minimal counterexample $G$ to the Four Colour Theorem, a degree-$5$ vertex $v$ of $G$ (equivalently a pentagonal face $F_v$ of $G' = \mathrm{dual}(G)$), and an index $i \in \{0,1,2,3,4\}$, the @@ -301,7 +301,7 @@ for every $t \in \{1, \dots, t^*\}$. \begin{thebibliography}{9} \bibitem{parent} -E.~Bauerfeld, \emph{Dual Decomposition of Minimal Counterexamples}. +E.~Bauerfeld, \emph{Face-Monochromatic Pairs and the Four Colour Theorem}. Companion paper. \end{thebibliography}