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didericis bd8526eb11 dual_decomposition: trim to the minimal-counterexample section
Remove the Introduction and Strategy sections and everything after the
separating-cycle definition (no-separating-triangle lemma, 5-connectivity
proposition, and the Step 2-6 stubs). Rename the section heading from
"Step 1: The minimal counterexample" to "The minimal counterexample", drop
the now-unused separating-cycle definition, and adjust the lead-in to mention
only the degree reduction. Remaining: reduction-to-triangulations lemma,
minimal-counterexample definition, |V|>=12 remark, and minimum-degree-5 lemma.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2026-05-22 18:28:32 -04:00

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\relax
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{The minimal counterexample}}{1}{}\protected@file@percent }
\newlabel{lem:triangulate}{{1.1}{1}}
\newlabel{def:minimal}{{1.2}{1}}
\newlabel{lem:mindeg}{{1.4}{1}}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{0pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\gdef \@abspage@last{2}