From b86df526ecc13708da2ffb1635b99850bad84e8a Mon Sep 17 00:00:00 2001 From: didericis Date: Fri, 22 May 2026 11:26:11 -0400 Subject: [PATCH] Keep only the resulting-duals figure at n=21 Remove the witness-ELG figure (former Fig. 5); keep the six resulting duals with their introduced green bridge edges. Fix the dangling cross-reference in the caption. Co-Authored-By: Claude Opus 4.7 --- .../figures/n21_elgs.png | Bin 679343 -> 0 bytes papers/even_level_graph_generators/paper.pdf | Bin 1620175 -> 1079927 bytes papers/even_level_graph_generators/paper.tex | 25 +++++------------- 3 files changed, 6 insertions(+), 19 deletions(-) delete mode 100644 papers/even_level_graph_generators/figures/n21_elgs.png diff --git a/papers/even_level_graph_generators/figures/n21_elgs.png b/papers/even_level_graph_generators/figures/n21_elgs.png deleted file mode 100644 index be985e884afe34206d11ec2850ef798187bead38..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 679343 zcmeFZXH-*LyEYsvih>0Z1pylTt4@Au~$PZ;j)UOTL;%r)nIUu~{nLw#)?Zb5Ds z4927L&-L3d*q%Wcj4N>0PH<$=vfmy2OW9NFp64Cc$DXK%Pi$a%4?W$STs@uat&V%y zJn^u1b-5rbe@^zY^l>{+Pd5)`IXUP5e21*-6I(g)8y)w-S$4bqbKe67I}#85*`kAd z9tGP1gXvtqa@RXyn!@GRHQKu|7kc`|>9^beslM5B`o#3)x2I_-#|LYS^NPBSSf%+U zd1khG$l?-uS2q6vQ{$Lz*RL}N;x%`@h^}2B63R9#lioy*B#fLs@n^xmYCgg3_e!(J 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The -dashed red edges are the same-parity edges that the bridge switches flip; -flipping them yields the corresponding dual in -Figure~\ref{fig:n21-duals}. Duals $1$ and $2$ are Even Level Graphs -outright, so no edge is flipped.} -\label{fig:n21-elgs} -\end{figure} - \begin{figure}[ht] \centering \includegraphics[width=\textwidth]{figures/n21_duals.png} \caption{The six Holton--McKay duals, drawn as crossing-free planar graphs -with the same parity colouring. The solid green edges are the bridge edges -introduced by the switches from the Even Level Graphs of -Figure~\ref{fig:n21-elgs}. Each green edge is a bridge of its parity -subgraph, so no new cycle -- and in particular no odd cycle -- is created; -duals $1$ and $2$ coincide with their Even Level Graphs and have no added -edge.} +and coloured by parity (blue even, orange odd, with respect to the fixed +level-parity labelling). The solid green edges are the bridge edges +introduced by the bridge switches from each dual's witness Even Level +Graph. Each green edge is a bridge of its parity subgraph, so no new cycle +-- and in particular no odd cycle -- is created; duals $1$ and $2$ coincide +with their Even Level Graphs and have no added edge.} \label{fig:n21-duals} \end{figure}

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