diff --git a/papers/colored_edge_flip_classes/paper.aux b/papers/colored_edge_flip_classes/paper.aux index d05375a..4b27593 100644 --- a/papers/colored_edge_flip_classes/paper.aux +++ b/papers/colored_edge_flip_classes/paper.aux @@ -6,7 +6,7 @@ \newlabel{def:flip-symmetric}{{3.1}{2}} \newlabel{def:flip-neighborhood}{{3.2}{2}} \newlabel{def:colored-flip-class}{{3.3}{2}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{A minimal four-colorable counterexample}}{2}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The flip neighborhood of a minimum-order counterexample}}{2}{}\protected@file@percent } \newlabel{def:edge-deletion}{{4.1}{2}} \newlabel{lem:edge-deletion-4colorable}{{4.2}{2}} \newlabel{lem:edge-deletion-coloring-structure}{{4.3}{3}} diff --git a/papers/colored_edge_flip_classes/paper.fdb_latexmk b/papers/colored_edge_flip_classes/paper.fdb_latexmk index adbad6c..161dbfb 100644 --- a/papers/colored_edge_flip_classes/paper.fdb_latexmk +++ b/papers/colored_edge_flip_classes/paper.fdb_latexmk @@ -1,5 +1,5 @@ # Fdb version 3 -["pdflatex"] 1778742998 "paper.tex" "paper.pdf" "paper" 1778742998 +["pdflatex"] 1778743050 "paper.tex" "paper.pdf" "paper" 1778743050 "/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 "" @@ -128,8 +128,8 @@ "/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1647878959 4410336 7d30a02e9fa9a16d7d1f8d037ba69641 "" "/usr/local/texlive/2022/texmf-var/web2c/pdftex/pdflatex.fmt" 1665017617 2826443 7e98410c533054b636c6470db83a27bc "" "/usr/local/texlive/2022/texmf.cnf" 1647878952 577 209b46be99c9075fd74d4c0369380e8c "" - "paper.aux" 1778742998 1730 4d7f3892dba90583ca8d3c50faea2157 "pdflatex" - "paper.tex" 1778742990 14020 e71c46937129b64f0afa621f9c03d8d9 "" + "paper.aux" 1778743050 1746 21946e155e8c5bd26d5d9b5107a85bfc "pdflatex" + "paper.tex" 1778743042 14036 c8b4296ad33d9dcc8aad020d28492369 "" (generated) "paper.aux" "paper.log" diff --git a/papers/colored_edge_flip_classes/paper.log b/papers/colored_edge_flip_classes/paper.log index 18be000..e246978 100644 --- a/papers/colored_edge_flip_classes/paper.log +++ b/papers/colored_edge_flip_classes/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) 14 MAY 2026 03:16 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 14 MAY 2026 03:17 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -526,7 +526,7 @@ b> usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb> -Output written on paper.pdf (4 pages, 212549 bytes). +Output written on paper.pdf (4 pages, 212852 bytes). PDF statistics: 105 PDF objects out of 1000 (max. 8388607) 64 compressed objects within 1 object stream diff --git a/papers/colored_edge_flip_classes/paper.pdf b/papers/colored_edge_flip_classes/paper.pdf index ab0f7c7..243a67c 100644 Binary files a/papers/colored_edge_flip_classes/paper.pdf and b/papers/colored_edge_flip_classes/paper.pdf differ diff --git a/papers/colored_edge_flip_classes/paper.tex b/papers/colored_edge_flip_classes/paper.tex index e27cbaa..31ed348 100644 --- a/papers/colored_edge_flip_classes/paper.tex +++ b/papers/colored_edge_flip_classes/paper.tex @@ -198,7 +198,7 @@ opposite vertices $w_i, x_i$ satisfy $\varphi(w_i) \neq \varphi(x_i)$. \end{definition} -\section{A minimal four-colorable counterexample} +\section{The flip neighborhood of a minimum-order counterexample} \begin{definition}[Edge-deletion subgraph]\label{def:edge-deletion} Let $G$ be a maximal planar graph and $uv \in E(G)$. The