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Split medial pigeonhole programme into its own paper

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Move Section 5 of "Medial Tire Decompositions of Plane Triangulations"
into a new standalone paper, "The Medial Pigeonhole Programme", which
cites the medial tire paper for its terminology and notation. Convert
the three cross-references that pointed into earlier sections (annular
teeth, bite-face-count, boundary medial vertices) into citations.

Remove Section 5 from the medial tire paper and update its abstract to
drop the moved chain-pigeonhole claim, pointing to the follow-up paper.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-06-14 21:08:06 -04:00
parent b2439e4bac
commit d3fc4bfc4c
10 changed files with 1656 additions and 384 deletions
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papers/medial_tire_decompositions_of_plane_triangulations/paper.aux
+10 -17
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@@ -1,4 +1,5 @@
\relax
\citation{bauerfeld-medial-pigeonhole}
\citation{bauerfeld-nested-tire-decompositions}
\citation{bauerfeld-nested-tire-decompositions}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{}\protected@file@percent }
@@ -13,7 +14,7 @@
\newlabel{thm:annular-medial-colour-bound}{{3.3}{3}}
\newlabel{def:annular-teeth}{{3.4}{3}}
\newlabel{rem:teeth-sharing}{{3.5}{3}}
\newlabel{rem:up-teeth-count}{{3.6}{3}}
\newlabel{rem:up-teeth-count}{{3.6}{4}}
\newlabel{def:bite}{{3.7}{4}}
\newlabel{rem:bite-face-count}{{3.8}{4}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A full medial tire graph $\mathsf {M}(T)$ illustrating the tooth terminology. The thick cycle is the annular medial cycle $A(T)$, whose black vertices are the annular medial vertices. Each edge of $A(T)$ carries one tooth: up teeth (blue apexes, outer-boundary medial vertices) point into the outer region, and down teeth (red apexes, inner-boundary medial vertices) point into the inner region. The two down teeth meeting at the central shared apex (larger red vertex) form a bite; that shared apex splits the inner region into two faces, one with four down teeth on its boundary and one with none.}}{4}{}\protected@file@percent }
@@ -26,25 +27,17 @@
\newlabel{fig:medial-annular-cycle-counterexample}{{3}{5}}
\newlabel{def:medial-restriction-relation}{{3.10}{5}}
\citation{bauerfeld-nested-tire-decompositions}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Decomposition}}{6}{}\protected@file@percent }
\newlabel{cor:medial-tire-decomposition}{{4.1}{6}}
\newlabel{def:compatible-family}{{4.2}{6}}
\newlabel{prop:gluing-criterion}{{4.3}{6}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{A medial pigeonhole programme}}{6}{}\protected@file@percent }
\newlabel{def:medial-boundary-state}{{5.1}{6}}
\newlabel{conj:medial-chain-pigeonhole}{{5.2}{7}}
\newlabel{conj:medial-route-fct}{{5.3}{7}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Kempe-cycle conservation across medial tires}}{7}{}\protected@file@percent }
\newlabel{lem:kempe-cycles}{{5.5}{7}}
\newlabel{lem:kempe-conservation}{{5.6}{8}}
\newlabel{def:kempe-balanced}{{5.7}{8}}
\newlabel{rem:kempe-balance-necessary}{{5.8}{8}}
\bibcite{bauerfeld-nested-tire-decompositions}{1}
\bibcite{tait-original}{2}
\bibcite{bauerfeld-medial-pigeonhole}{2}
\bibcite{tait-original}{3}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{12.7778pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{29.38873pt}
\newlabel{tocindent3}{0pt}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{11}{}\protected@file@percent }
\gdef \@abspage@last{11}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Decomposition}}{6}{}\protected@file@percent }
\newlabel{cor:medial-tire-decomposition}{{4.1}{6}}
\newlabel{def:compatible-family}{{4.2}{6}}
\newlabel{prop:gluing-criterion}{{4.3}{6}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{6}{}\protected@file@percent }
\gdef \@abspage@last{6}