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 $\OML/cmm/m/it/10 A \OT1/cmr/m/n/10 = (\OML/cmm/m/it/10 A[]; A[]; A[]; A[]; A[]\OT1/cmr/m/n/10 )$. [] - +[3] + File: fig_reduced_dual_step1.png Graphic file (type png) Package pdftex.def Info: fig_reduced_dual_step1.png used on input line 253. (pdftex.def) Requested size: 172.79846pt x 166.55775pt. - + File: fig_reduced_dual_step2.png Graphic file (type png) Package pdftex.def Info: fig_reduced_dual_step2.png used on input line 254. (pdftex.def) Requested size: 172.79846pt x 170.39505pt. - + File: fig_reduced_dual_step3.png Graphic file (type png) Package pdftex.def Info: fig_reduced_dual_step3.png used on input line 255. (pdftex.def) Requested size: 172.79846pt x 170.39505pt. - + File: fig_reduced_dual_step4.png Graphic file (type png) Package pdftex.def Info: fig_reduced_dual_step4.png used on input line 256. (pdftex.def) Requested size: 172.79846pt x 171.44409pt. - -LaTeX Warning: `h' float specifier changed to `ht'. - -[3] [4 <./fig_reduced_dual_step1.png> <./fig_reduced_dual_step2.png> <./fig_red -uced_dual_step3.png> <./fig_reduced_dual_step4.png>] - + [4 <./fig_reduced_dual_step1.png> <./fig_reduced_dual_step2.png> <./fig_reduce +d_dual_step3.png> <./fig_reduced_dual_step4.png>] [5] + File: fig_chord_apex_step1.png Graphic file (type png) Package pdftex.def Info: fig_chord_apex_step1.png used on input line 377. (pdftex.def) Requested size: 251.9989pt x 250.5104pt. - + File: fig_chord_apex_step2.png Graphic file (type png) Package pdftex.def Info: fig_chord_apex_step2.png used on input line 378. (pdftex.def) Requested size: 172.79846pt x 176.08986pt. - + File: fig_chord_apex_step3.png Graphic file (type png) Package pdftex.def Info: fig_chord_apex_step3.png used on input line 379. @@ -243,16 +244,20 @@ Package pdftex.def Info: fig_chord_apex_step3.png used on input line 379. LaTeX Warning: `h' float specifier changed to `ht'. -[5] [6 <./fig_chord_apex_step1.png> <./fig_chord_apex_step2.png> <./fig_chord_a -pex_step3.png>] [7] +[6] [7 <./fig_chord_apex_step1.png> <./fig_chord_apex_step2.png> <./fig_chord_a +pex_step3.png>] File: fig_cubic_edge_contraction.png Graphic file (type png) Package pdftex.def Info: fig_cubic_edge_contraction.png used on input line 522 . (pdftex.def) Requested size: 341.9989pt x 73.08138pt. - [8 <./fig_cubic_edge_contraction.png>] - + + +LaTeX Warning: `h' float specifier changed to `ht'. + +[8] + File: fig_thm_cubic_contraction_4face.png Graphic file (type png) Package pdftex.def Info: fig_thm_cubic_contraction_4face.png used on input lin @@ -262,8 +267,8 @@ e 597. LaTeX Warning: `h' float specifier changed to `ht'. -[9] -Underfull \vbox (badness 10000) has occurred while \output is active [] +[9 <./fig_cubic_edge_contraction.png>] +Underfull \vbox (badness 1242) has occurred while \output is active [] [10 <./fig_thm_cubic_contraction_4face.png>] Underfull \hbox (badness 1648) in paragraph at lines 721--727 @@ -310,7 +315,7 @@ cal/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb> -Output written on paper.pdf (12 pages, 1017869 bytes). +Output written on paper.pdf (12 pages, 1018017 bytes). PDF statistics: 183 PDF objects out of 1000 (max. 8388607) 101 compressed objects within 2 object streams diff --git a/papers/dual_decomposition_minimal_counterexamples/paper.pdf b/papers/face_monochromatic_pairs/paper.pdf similarity index 92% rename from papers/dual_decomposition_minimal_counterexamples/paper.pdf rename to papers/face_monochromatic_pairs/paper.pdf index 7de5f50..f78250f 100644 Binary files a/papers/dual_decomposition_minimal_counterexamples/paper.pdf and b/papers/face_monochromatic_pairs/paper.pdf differ diff --git a/papers/dual_decomposition_minimal_counterexamples/paper.tex b/papers/face_monochromatic_pairs/paper.tex similarity index 99% rename from papers/dual_decomposition_minimal_counterexamples/paper.tex rename to papers/face_monochromatic_pairs/paper.tex index a855fc8..7f94416 100644 --- a/papers/dual_decomposition_minimal_counterexamples/paper.tex +++ b/papers/face_monochromatic_pairs/paper.tex @@ -26,7 +26,7 @@ \begin{document} -\title{Dual Decomposition of Minimal Counterexamples} +\title{Face-Monochromatic Pairs and the Four Colour Theorem} % author one information \author{Eric Bauerfeld} diff --git a/papers/dual_decomposition_iterated_reduction/experiments/draw_iterated_reduction.py b/papers/iterated_reduction_in_reduced_dual/experiments/draw_iterated_reduction.py similarity index 100% rename from papers/dual_decomposition_iterated_reduction/experiments/draw_iterated_reduction.py rename to papers/iterated_reduction_in_reduced_dual/experiments/draw_iterated_reduction.py diff --git a/papers/dual_decomposition_iterated_reduction/experiments/draw_iterated_reduction_n14.py b/papers/iterated_reduction_in_reduced_dual/experiments/draw_iterated_reduction_n14.py similarity index 100% rename from papers/dual_decomposition_iterated_reduction/experiments/draw_iterated_reduction_n14.py rename to papers/iterated_reduction_in_reduced_dual/experiments/draw_iterated_reduction_n14.py diff --git a/papers/dual_decomposition_iterated_reduction/fig_alg_step0.png b/papers/iterated_reduction_in_reduced_dual/fig_alg_step0.png similarity index 100% rename from papers/dual_decomposition_iterated_reduction/fig_alg_step0.png rename to papers/iterated_reduction_in_reduced_dual/fig_alg_step0.png diff --git a/papers/dual_decomposition_iterated_reduction/fig_alg_step1.png b/papers/iterated_reduction_in_reduced_dual/fig_alg_step1.png similarity index 100% rename from papers/dual_decomposition_iterated_reduction/fig_alg_step1.png rename to papers/iterated_reduction_in_reduced_dual/fig_alg_step1.png diff --git a/papers/dual_decomposition_iterated_reduction/fig_alg_step2.png b/papers/iterated_reduction_in_reduced_dual/fig_alg_step2.png similarity index 100% rename from papers/dual_decomposition_iterated_reduction/fig_alg_step2.png rename to papers/iterated_reduction_in_reduced_dual/fig_alg_step2.png diff --git a/papers/dual_decomposition_iterated_reduction/paper.aux b/papers/iterated_reduction_in_reduced_dual/paper.aux similarity index 100% rename from papers/dual_decomposition_iterated_reduction/paper.aux rename to papers/iterated_reduction_in_reduced_dual/paper.aux diff --git a/papers/dual_decomposition_iterated_reduction/paper.log b/papers/iterated_reduction_in_reduced_dual/paper.log similarity index 98% rename from papers/dual_decomposition_iterated_reduction/paper.log rename to papers/iterated_reduction_in_reduced_dual/paper.log index d7abe64..bd30b66 100644 --- a/papers/dual_decomposition_iterated_reduction/paper.log +++ b/papers/iterated_reduction_in_reduced_dual/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 13:51 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 24 MAY 2026 15:04 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -220,7 +220,7 @@ Here is how much of TeX's memory you used: 21067 multiletter control sequences out of 15000+600000 475834 words of font info for 54 fonts, out of 8000000 for 9000 1302 hyphenation exceptions out of 8191 - 69i,7n,76p,1399b,294s stack positions out of 10000i,1000n,20000p,200000b,200000s + 69i,7n,76p,1255b,294s stack positions out of 10000i,1000n,20000p,200000b,200000s -Output written on paper.pdf (4 pages, 387470 bytes). +Output written on paper.pdf (4 pages, 385985 bytes). PDF statistics: 109 PDF objects out of 1000 (max. 8388607) 62 compressed objects within 1 object stream diff --git a/papers/dual_decomposition_iterated_reduction/paper.pdf b/papers/iterated_reduction_in_reduced_dual/paper.pdf similarity index 82% rename from papers/dual_decomposition_iterated_reduction/paper.pdf rename to papers/iterated_reduction_in_reduced_dual/paper.pdf index 7de74e7..0f246d5 100644 Binary files a/papers/dual_decomposition_iterated_reduction/paper.pdf and b/papers/iterated_reduction_in_reduced_dual/paper.pdf differ diff --git a/papers/dual_decomposition_iterated_reduction/paper.tex b/papers/iterated_reduction_in_reduced_dual/paper.tex similarity index 98% rename from papers/dual_decomposition_iterated_reduction/paper.tex rename to papers/iterated_reduction_in_reduced_dual/paper.tex index 62bf5a7..01f2965 100644 --- a/papers/dual_decomposition_iterated_reduction/paper.tex +++ b/papers/iterated_reduction_in_reduced_dual/paper.tex @@ -26,7 +26,7 @@ \begin{document} -\title{Iterated Reduction of Dual Minimal Counterexamples} +\title{An Iterated Reduction in the Reduced Dual} \author{Eric Bauerfeld} \address{} @@ -53,8 +53,8 @@ $3$-edge-colouring} \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}