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 <noreply@anthropic.com>
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2026-05-22 11:26:11 -04:00
parent b3998fbdb3
commit b86df526ec
3 changed files with 6 additions and 19 deletions
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@@ -426,29 +426,16 @@ witnesses are step-verified.}
\label{tab:n21}
\end{table}
\begin{figure}[ht]
\centering
\includegraphics[width=\textwidth]{figures/n21_elgs.png}
\caption{The witness Even Level Graph for each of the six Holton--McKay
duals, drawn as a crossing-free planar graph and coloured by parity (blue
even, orange odd, with respect to the fixed level-parity labelling). 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}