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a/papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2_levels.png b/papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2_levels.png new file mode 100644 index 0000000..2599b0a Binary files /dev/null and b/papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2_levels.png differ diff --git a/papers/level_resolutions_of_maximal_planar_graphs/paper.aux b/papers/level_resolutions_of_maximal_planar_graphs/paper.aux index 99335d7..831468a 100644 --- a/papers/level_resolutions_of_maximal_planar_graphs/paper.aux +++ b/papers/level_resolutions_of_maximal_planar_graphs/paper.aux @@ -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}{}} \@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Computational evidence}}{3}{section.5}\protected@file@percent } 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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). 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