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level_resolutions: add n=7 missing-isomorphism figures, rebuild PDF

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Add the figures for the n=7, idx=2 missing-isomorphism case
(missing_iso_n7_idx2.png is included in paper.tex), plus its
4-coloring and level-decomposition companions and the G-for-T
preimage graph. Rebuild paper.pdf and its LaTeX aux/log/out.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-22 10:54:07 -04:00
parent 984655fd3d
commit 30f28a60d6
8 changed files with 119 additions and 67 deletions
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papers/level_resolutions_of_maximal_planar_graphs/paper.aux
+13 -15
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@@ -29,7 +29,7 @@
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The four-color conjecture via level resolutions}}{3}{section.4}\protected@file@percent }
\newlabel{conj:preimage}{{4.1}{3}{Resolution preimage}{theorem.4.1}{}}
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\newlabel{tab:coverage}{{1}{4}{Iso-class coverage under the level-resolution definition}{table.1}{}}
@@ -37,7 +37,7 @@
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\newlabel{obs:icosa}{{5.2}{4}{}{theorem.5.2}{}}
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\newlabel{conj:md4}{{5.3}{4}{$\mathrm {md}_4$ surjectivity}{theorem.5.3}{}}
\newlabel{conj:md5}{{5.3}{4}{$\mathrm {md}_5$ surjectivity}{theorem.5.3}{}}
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@@ -51,16 +51,16 @@
\newlabel{def:simple-level-resolution}{{6.4}{6}{Simple level resolution}{theorem.6.4}{}}
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\newlabel{conj:simple-md4}{{6.7}{7}{Simple-resolution $\mathrm {md}_4$ surjectivity}{theorem.6.7}{}}
\newlabel{sec:contraction-lift}{{6.7}{7}{Towards a proof: a contraction--lift strategy}{subsection.6.7}{}}
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\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{Coverage test.}}{6}{section*.2}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Simple-resolution coverage under the algorithm of Section\nonbreakingspace \ref {sec:flip-algorithm}. ``Algorithm output (any)'' counts iso-classes that appear as the iso-class of some labelled triangulation output of the algorithm; ``Simple level resolutions'' counts iso-classes that additionally satisfy the bipartite-parity condition of Definition\nonbreakingspace \ref {def:simple-level-resolution}.}}{7}{table.2}\protected@file@percent }
\newlabel{tab:simple-coverage}{{2}{7}{Simple-resolution coverage under the algorithm of Section~\ref {sec:flip-algorithm}. ``Algorithm output (any)'' counts iso-classes that appear as the iso-class of some labelled triangulation output of the algorithm; ``Simple level resolutions'' counts iso-classes that additionally satisfy the bipartite-parity condition of Definition~\ref {def:simple-level-resolution}}{table.2}{}}
\newlabel{obs:md5-simple-resolution}{{6.6}{7}{}{theorem.6.6}{}}
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\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Discussion and open questions}}{7}{section.7}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces At $n = 7$, iso-class $T$ with degree sequence $(6, 5, 5, 5, 3, 3, 3)$ is not a simple level resolution. Left: $T$ drawn with face source $S = \{0, 1, 5\}$ outlined; vertices are labelled by their BFS level. Middle: the even-parity subgraph $E_{T,S}(T)$, induced on $\{0, 1, 5\}$, contains the source-face triangle (highlighted) — an odd cycle. Right: the odd-parity subgraph $O_{T,S}(T)$, induced on $\{2, 3, 4, 6\}$, contains a triangle on $\{2, 3, 6\}$ (highlighted). The obstruction is identical for every face source of $T$; vertex sources at degree-$3$ vertices produce $L_1$ triangles in the odd-parity subgraph.}}{8}{figure.1}\protected@file@percent }
\newlabel{fig:missing-iso}{{1}{8}{At $n = 7$, iso-class $T$ with degree sequence $(6, 5, 5, 5, 3, 3, 3)$ is not a simple level resolution. Left: $T$ drawn with face source $S = \{0, 1, 5\}$ outlined; vertices are labelled by their BFS level. Middle: the even-parity subgraph $E_{T,S}(T)$, induced on $\{0, 1, 5\}$, contains the source-face triangle (highlighted) — an odd cycle. Right: the odd-parity subgraph $O_{T,S}(T)$, induced on $\{2, 3, 4, 6\}$, contains a triangle on $\{2, 3, 6\}$ (highlighted). The obstruction is identical for every face source of $T$; vertex sources at degree-$3$ vertices produce $L_1$ triangles in the odd-parity subgraph}{figure.1}{}}
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\newlabel{sec:impl}{{8}{8}{Implementation}{section.8}{}}
\bibcite{appelhaken}{1}
\bibcite{rsst}{2}
\bibcite{tutte}{3}
@@ -70,7 +70,5 @@
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\gdef \@abspage@last{9}