diff --git a/.gitignore b/.gitignore index 6e6f65b..b9bfdd3 100644 --- a/.gitignore +++ b/.gitignore @@ -7,3 +7,5 @@ colored_pentagon_reduction/data/ __pycache__/ *.pyc *.pyo +.claude/ +*.synctex.gz diff --git a/papers/plane_diamond_coloring/paper.aux b/papers/plane_diamond_coloring/paper.aux index 4e82dd7..3a542cc 100644 --- a/papers/plane_diamond_coloring/paper.aux +++ b/papers/plane_diamond_coloring/paper.aux @@ -5,9 +5,9 @@ \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Notation}}{1}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Definitions}}{1}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Results}}{1}{}\protected@file@percent } -\bibcite{appel1977every}{1} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The unique smallest maximal planar graph with no plane diamond coloring; it has $13$ vertices and degree sequence $(6,6,6,6,6,6,6,5,5,4,4,3,3)$.}}{2}{}\protected@file@percent } \newlabel{fig:counterexample}{{1}{2}} +\bibcite{appel1977every}{1} \bibcite{robertson1997four}{2} \bibcite{mckaygraph6}{3} \newlabel{tocindent-1}{0pt} diff --git a/papers/plane_diamond_coloring/paper.fdb_latexmk b/papers/plane_diamond_coloring/paper.fdb_latexmk index aea99d3..71fadc2 100644 --- a/papers/plane_diamond_coloring/paper.fdb_latexmk +++ b/papers/plane_diamond_coloring/paper.fdb_latexmk @@ -1,5 +1,6 @@ # Fdb version 3 -["pdflatex"] 1778346213 "paper.tex" "paper.pdf" "paper" 1778346214 +["pdflatex"] 1778347081 "/Users/didericis/Code/math-research/papers/plane_diamond_coloring/paper.tex" "paper.pdf" "paper" 1778347082 + "/Users/didericis/Code/math-research/papers/plane_diamond_coloring/paper.tex" 1778347081 7877 4504fbad3843f8cebeb3943b86c7fcee "" "/usr/local/texlive/2022/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 "" @@ -61,8 +62,8 @@ "/usr/local/texlive/2022/texmf-var/web2c/pdftex/pdflatex.fmt" 1665017617 2826443 7e98410c533054b636c6470db83a27bc "" "/usr/local/texlive/2022/texmf.cnf" 1647878952 577 209b46be99c9075fd74d4c0369380e8c "" "counterexample.png" 1778345471 31680 49acd944c061e194d20aac1d5cd8ef86 "" - "paper.aux" 1778346214 1030 91a64fb2301d318c3529a163b199f774 "pdflatex" - "paper.tex" 1778346203 7393 d95c3a990ad0a8a45120d7bebb561308 "" + "paper.aux" 1778347082 1030 fa34fda9f562babd4bf0c5868b521a80 "pdflatex" + "paper.tex" 1778347081 7877 4504fbad3843f8cebeb3943b86c7fcee "" (generated) "paper.aux" "paper.log" diff --git a/papers/plane_diamond_coloring/paper.fls b/papers/plane_diamond_coloring/paper.fls index 9d05727..aca8a20 100644 --- a/papers/plane_diamond_coloring/paper.fls +++ b/papers/plane_diamond_coloring/paper.fls @@ -2,7 +2,7 @@ PWD /Users/didericis/Code/math-research/papers/plane_diamond_coloring INPUT /usr/local/texlive/2022/texmf.cnf INPUT /usr/local/texlive/2022/texmf-dist/web2c/texmf.cnf INPUT /usr/local/texlive/2022/texmf-var/web2c/pdftex/pdflatex.fmt -INPUT paper.tex +INPUT /Users/didericis/Code/math-research/papers/plane_diamond_coloring/paper.tex OUTPUT paper.log INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls diff --git a/papers/plane_diamond_coloring/paper.log b/papers/plane_diamond_coloring/paper.log index ce4ec80..b92f819 100644 --- a/papers/plane_diamond_coloring/paper.log +++ b/papers/plane_diamond_coloring/paper.log @@ -1,12 +1,12 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 9 MAY 2026 13:03 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 9 MAY 2026 13:18 entering extended mode restricted \write18 enabled. + file:line:error style messages enabled. %&-line parsing enabled. -**paper.tex -(./paper.tex +**/Users/didericis/Code/math-research/papers/plane_diamond_coloring/paper.tex +(/Users/didericis/Code/math-research/papers/plane_diamond_coloring/paper.tex LaTeX2e <2021-11-15> patch level 1 -L3 programming layer <2022-02-24> -(/usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls +L3 programming layer <2022-02-24> (/usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls Document Class: amsart 2020/05/29 v2.20.6 \linespacing=\dimen138 \normalparindent=\dimen139 @@ -18,17 +18,14 @@ Package: amsmath 2021/10/15 v2.17l AMS math features For additional information on amsmath, use the `?' option. (/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty Package: amstext 2021/08/26 v2.01 AMS text - -(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty + (/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 generic functions \@emptytoks=\toks16 \ex@=\dimen140 -)) -(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty +)) (/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d Bold Symbols \pmbraise@=\dimen141 -) -(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty +) (/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty Package: amsopn 2021/08/26 v2.02 operator names ) \inf@bad=\count185 @@ -69,13 +66,10 @@ LaTeX Font Info: Redeclaring font encoding OMS on input line 744. LaTeX Info: Redefining \[ on input line 2938. LaTeX Info: Redefining \] on input line 2939. ) -LaTeX Font Info: Trying to load font information for U+msa on input line 397 -. - -(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd +LaTeX Font Info: Trying to load font information for U+msa on input line 397. + (/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2013/01/14 v3.01 AMS symbols A -) -(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty +) (/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 @@ -106,43 +100,34 @@ LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' \thm@postskip=\skip55 \thm@headsep=\skip56 \dth@everypar=\toks26 -) -(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty +) (/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR) - -(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty + (/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty Package: keyval 2014/10/28 v1.15 key=value parser (DPC) \KV@toks@=\toks27 -) -(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty +) (/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty Package: graphics 2021/03/04 v1.4d Standard LaTeX Graphics (DPC,SPQR) - -(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty + (/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty Package: trig 2021/08/11 v1.11 sin cos tan (DPC) -) -(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +) (/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration ) Package graphics Info: Driver file: pdftex.def on input line 107. - -(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def + (/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def File: pdftex.def 2020/10/05 v1.2a Graphics/color driver for pdftex )) \Gin@req@height=\dimen150 \Gin@req@width=\dimen151 -) -(/usr/local/texlive/2022/texmf-dist/tex/latex/url/url.sty +) (/usr/local/texlive/2022/texmf-dist/tex/latex/url/url.sty \Urlmuskip=\muskip17 Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. ) \c@theorem=\count272 - -(/usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def + (/usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def File: l3backend-pdftex.def 2022-02-07 L3 backend support: PDF output (pdfTeX) \l__color_backend_stack_int=\count273 \l__pdf_internal_box=\box53 -) -(./paper.aux) +) (./paper.aux) \openout1 = `paper.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 57. @@ -160,17 +145,13 @@ LaTeX Font Info: ... okay on input line 57. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 57. LaTeX Font Info: ... okay on input line 57. LaTeX Font Info: Trying to load font information for U+msa on input line 57. - (/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2013/01/14 v3.01 AMS symbols A ) LaTeX Font Info: Trying to load font information for U+msb on input line 57. - - -(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd + (/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B -) -(/usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii +) (/usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii [Loading MPS to PDF converter (version 2006.09.02).] \scratchcounter=\count274 \scratchdimen=\dimen152 @@ -185,46 +166,26 @@ File: umsb.fd 2013/01/14 v3.01 AMS symbols B \everyMPtoPDFconversion=\toks29 ) (/usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf -Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4 -85. - -(/usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg -File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv -e -)) -[1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] +Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 485. + (/usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live +)) [1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] File: counterexample.png Graphic file (type png) Package pdftex.def Info: counterexample.png used on input line 144. (pdftex.def) Requested size: 161.9989pt x 162.34474pt. - -[2 <./counterexample.png>] [3] (./paper.aux) ) + [2 <./counterexample.png>] [3] (./paper.aux) ) Here is how much of TeX's memory you used: - 2669 strings out of 478268 - 38618 string characters out of 5846347 + 2670 strings out of 478268 + 38814 string characters out of 5846347 339139 words of memory out of 5000000 20714 multiletter control sequences out of 15000+600000 476338 words of font info for 57 fonts, out of 8000000 for 9000 1302 hyphenation exceptions out of 8191 - 69i,8n,76p,770b,362s stack positions out of 10000i,1000n,20000p,200000b,200000s - -Output written on paper.pdf (3 pages, 215556 bytes). + 69i,8n,76p,836b,344s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on paper.pdf (3 pages, 216857 bytes). PDF statistics: 92 PDF objects out of 1000 (max. 8388607) 54 compressed objects within 1 object stream diff --git a/papers/plane_diamond_coloring/paper.pdf b/papers/plane_diamond_coloring/paper.pdf index b14a280..90dc46d 100644 Binary files a/papers/plane_diamond_coloring/paper.pdf and b/papers/plane_diamond_coloring/paper.pdf differ diff --git a/papers/plane_diamond_coloring/paper.tex b/papers/plane_diamond_coloring/paper.tex index 0963d9c..44edda5 100644 --- a/papers/plane_diamond_coloring/paper.tex +++ b/papers/plane_diamond_coloring/paper.tex @@ -146,6 +146,14 @@ For minimality and uniqueness, we exhaustively enumerated every maximal planar g \label{fig:counterexample} \end{figure} +\begin{conjecture} +Every maximal planar graph $G$ of minimum degree at least $5$ has a plane diamond coloring. +\end{conjecture} + +\begin{remark} +We have verified Conjecture 2.4 computationally for all maximal planar graphs of minimum degree at least $5$ and order at most $N$, by exhaustive enumeration via \texttt{Sage}'s \texttt{graphs.planar\_graphs} generator and the auxiliary-graph reduction described in the proof of Theorem 2.3. No counterexample has been found. +\end{remark} + \begin{thebibliography}{9} \bibitem{appel1977every} diff --git a/plane_diamond_coloring.py b/plane_diamond_coloring.py index b64d803..b7dd374 100644 --- a/plane_diamond_coloring.py +++ b/plane_diamond_coloring.py @@ -81,6 +81,26 @@ def search_counterexample_comprehensive(max_order: int, min_order: int = 4) -> l return counterexamples +def search_min_degree_counterexample_comprehensive(max_order: int, minimum_degree: int, min_order: int = 4) -> list[Graph]: + """ + Iterate through every maximal planar graph of order in [min_order, max_order] + with the given minimum degree, and return all those without a plane diamond + coloring. + """ + counterexamples: list[Graph] = [] + for n in range(min_order, max_order + 1): + checked = 0 + for g in graphs.planar_graphs(n, minimum_connectivity=3, maximum_face_size=3, minimum_degree=minimum_degree): + checked += 1 + if not has_plane_diamond_coloring(g): + print(f"Counterexample at order {n}, min_degree {minimum_degree} (graph #{checked}): {g.graph6_string()}") + counterexamples.append(g) + if checked % 100 == 0: + print(f" order {n}: checked {checked} graphs, {len(counterexamples)} counterexamples so far") + print(f"order {n} done: {checked} triangulations of min degree {minimum_degree} checked") + return counterexamples + + if __name__ == "__main__": import sys if len(sys.argv) > 1 and sys.argv[1] == "comprehensive": @@ -90,6 +110,14 @@ if __name__ == "__main__": print(f"Found {len(counterexamples)} counterexamples in orders {min_order}..{max_order}") for g in counterexamples: canonize_and_save_graph(g) + elif len(sys.argv) > 1 and sys.argv[1] == "min-degree": + max_order = int(sys.argv[2]) if len(sys.argv) > 2 else 13 + minimum_degree = int(sys.argv[3]) if len(sys.argv) > 3 else 5 + min_order = int(sys.argv[4]) if len(sys.argv) > 4 else 4 + counterexamples = search_min_degree_counterexample_comprehensive(max_order, minimum_degree, min_order) + print(f"Found {len(counterexamples)} counterexamples in orders {min_order}..{max_order} with min degree {minimum_degree}") + for g in counterexamples: + canonize_and_save_graph(g) else: n = int(sys.argv[1]) if len(sys.argv) > 1 else 12 num_trials = int(sys.argv[2]) if len(sys.argv) > 2 else 100