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} \label{tab:n21}
\end{table} \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] \begin{figure}[ht]
\centering \centering
\includegraphics[width=\textwidth]{figures/n21_duals.png} \includegraphics[width=\textwidth]{figures/n21_duals.png}
\caption{The six Holton--McKay duals, drawn as crossing-free planar graphs \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 and coloured by parity (blue even, orange odd, with respect to the fixed
introduced by the switches from the Even Level Graphs of level-parity labelling). The solid green edges are the bridge edges
Figure~\ref{fig:n21-elgs}. Each green edge is a bridge of its parity introduced by the bridge switches from each dual's witness Even Level
subgraph, so no new cycle -- and in particular no odd cycle -- is created; Graph. Each green edge is a bridge of its parity subgraph, so no new cycle
duals $1$ and $2$ coincide with their Even Level Graphs and have no added -- and in particular no odd cycle -- is created; duals $1$ and $2$ coincide
edge.} with their Even Level Graphs and have no added edge.}
\label{fig:n21-duals} \label{fig:n21-duals}
\end{figure} \end{figure}