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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
Download Patch File Download Diff File Expand all files Collapse all files
papers/level_resolutions_of_maximal_planar_graphs/G_for_T_n7_idx2.png
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papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2.png
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papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2_4color.png
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papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2_levels.png
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papers/level_resolutions_of_maximal_planar_graphs/paper.aux
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@@ -29,7 +29,7 @@
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@@ -51,16 +51,16 @@
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\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}{}}
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\@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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papers/level_resolutions_of_maximal_planar_graphs/paper.log
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\OT1/cmr/m/n/10 Equiv-a-lently, ev-ery max-i-mal pla-nar graph (tri-an-gu-la-ti
on) is 4-colorable. The Appel--
[]
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\OT1/cmr/m/n/10 Haken proof [[]] and sub-se-quent Robertson--Sanders--Seymour--
Thomas re-fine-ment [[]]
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\OT1/cmr/m/n/10 rely on dis-charg-ing ar-gu-ments and computer-verified re-duci
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papers/level_resolutions_of_maximal_planar_graphs/paper.pdf
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