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Add Heawood chain-pigeonhole programme to tire-dual paper

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Define a +/-1 Heawood face-labelling of a tire, its induced boundary
Heawood sequences and restriction relation, and interface compatibility
(0<->0, +1<->-1 = vertex face-sum vanishes mod 3). State the Heawood
chain-pigeonhole conjecture and a tire route to the Four Colour Theorem,
parallel to the medial programme.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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didericis
2026-06-17 00:45:03 -04:00
parent 851ca7fbed
commit 251c453437
4 changed files with 186 additions and 29 deletions
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papers/heawood_restrictions_on_nested_tire_graph_duals/paper.aux
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\citation{bauerfeld-nested-tires}
\citation{bauerfeld-nested-tires}
\citation{bauerfeld-nested-tires}
\citation{Heawood1898}
\citation{bauerfeld-medial-tires}
\citation{bauerfeld-nested-tires}
\citation{bauerfeld-nested-tires}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{}\protected@file@percent }
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\newlabel{sec:heawood-restrictions}{{2}{2}}
\newlabel{def:heawood-labelling}{{2.1}{2}}
\newlabel{rem:no-interior-constraint}{{2.2}{2}}
\newlabel{def:boundary-sequences}{{2.3}{2}}
\newlabel{def:heawood-compatible}{{2.4}{2}}
\bibcite{Heawood1898}{1}
\bibcite{bauerfeld-depth}{2}
\bibcite{bauerfeld-nested-tires}{3}
\bibcite{bauerfeld-nested-tire-duals}{4}
\bibcite{bauerfeld-medial-tires}{4}
\bibcite{bauerfeld-nested-tire-duals}{5}
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\newlabel{rem:compat-is-heawood}{{2.5}{3}}
\newlabel{eq:heawood-face-sum-dual}{{2.1}{3}}
\newlabel{conj:heawood-chain-pigeonhole}{{2.6}{3}}
\newlabel{conj:heawood-route-fct}{{2.7}{3}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{3}{}\protected@file@percent }
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