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>
This commit is contained in:
@@ -1,20 +1,11 @@
|
||||
\relax
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{}\protected@file@percent }
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Strategy}}{1}{}\protected@file@percent }
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Step 1: The minimal counterexample}}{2}{}\protected@file@percent }
|
||||
\newlabel{lem:triangulate}{{3.1}{2}}
|
||||
\newlabel{def:minimal}{{3.2}{2}}
|
||||
\newlabel{lem:mindeg}{{3.4}{2}}
|
||||
\@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}
|
||||
\newlabel{lem:no-sep-tri}{{3.6}{3}}
|
||||
\newlabel{prop:5conn}{{3.7}{3}}
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Step 2: The dual cubic graph}}{3}{}\protected@file@percent }
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Step 3: The minimum edge cut}}{3}{}\protected@file@percent }
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Step 4: Capping to cubic planar graphs}}{3}{}\protected@file@percent }
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Step 5: Colouring the pieces}}{3}{}\protected@file@percent }
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{8}{Step 6: Reconnecting the colourings}}{3}{}\protected@file@percent }
|
||||
\gdef \@abspage@last{3}
|
||||
\gdef \@abspage@last{2}
|
||||
|
||||
Reference in New Issue
Block a user