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Rename section 4: the section's content is the flip neighborhood

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"A minimal four-colorable counterexample" reads as "a minimal
counterexample that is itself 4-colorable", which contradicts the
section's standing hypothesis $\chi(G_0) \geq 5$.  The section's
content is the structure of the flip neighborhood (and the colored
flip classes of its members) under that hypothesis, so name it that.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-14 03:17:45 -04:00
parent 31dd217863
commit a856c628f2
5 changed files with 7 additions and 7 deletions
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papers/colored_edge_flip_classes/paper.aux
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@@ -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}}
papers/colored_edge_flip_classes/paper.fdb_latexmk
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@@ -128,8 +128,8 @@
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"paper.aux"
"paper.log"
papers/colored_edge_flip_classes/paper.log
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@@ -526,7 +526,7 @@ b></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb>
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Output written on paper.pdf (4 pages, 212852 bytes).
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papers/colored_edge_flip_classes/paper.pdf
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papers/colored_edge_flip_classes/paper.tex
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@@ -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