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Account for the outer face in the Heawood face-sum identity

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The bounded-face sum omits the outer face at outer-boundary vertices, so
restrict the gluing identity to interior vertices (where all cluster
interfaces live) and recover a colouring by carrying a single +/-1 label
on the unbounded face f_inf, giving Heawood's identity on the full cubic
dual for the Tait step.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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didericis
2026-06-17 01:33:07 -04:00
parent c5f81842c7
commit 351ae0cdfe
4 changed files with 56 additions and 42 deletions
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papers/heawood_restrictions_on_nested_tire_graph_duals/paper.aux
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@@ -25,11 +25,15 @@
\newlabel{rem:no-interior-constraint}{{3.2}{3}}
\newlabel{def:boundary-sequences}{{3.3}{3}}
\newlabel{def:heawood-compatible}{{3.4}{3}}
\citation{Heawood1898}
\newlabel{rem:compat-is-heawood}{{3.5}{4}}
\newlabel{eq:heawood-face-sum-dual}{{3.1}{4}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Why the programme runs between nested clusters}}{4}{}\protected@file@percent }
\newlabel{prop:two-sided-decomposition}{{3.6}{4}}
\bibcite{Heawood1898}{1}
\newlabel{rem:why-clusters}{{3.7}{5}}
\newlabel{conj:heawood-chain-pigeonhole}{{3.8}{5}}
\newlabel{conj:heawood-route-fct}{{3.9}{5}}
\bibcite{bauerfeld-depth}{2}
\bibcite{bauerfeld-nested-tires}{3}
\bibcite{bauerfeld-medial-tires}{4}
@@ -39,8 +43,5 @@
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\newlabel{rem:why-clusters}{{3.7}{5}}
\newlabel{conj:heawood-chain-pigeonhole}{{3.8}{5}}
\newlabel{conj:heawood-route-fct}{{3.9}{5}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{5}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{6}{}\protected@file@percent }
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