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 be985e8..0000000 Binary files a/papers/even_level_graph_generators/figures/n21_elgs.png and /dev/null differ diff --git a/papers/even_level_graph_generators/paper.pdf b/papers/even_level_graph_generators/paper.pdf index f1f96b1..2c98eca 100644 Binary files a/papers/even_level_graph_generators/paper.pdf and b/papers/even_level_graph_generators/paper.pdf differ diff --git a/papers/even_level_graph_generators/paper.tex b/papers/even_level_graph_generators/paper.tex index d6a215b..3bebd3b 100644 --- a/papers/even_level_graph_generators/paper.tex +++ b/papers/even_level_graph_generators/paper.tex @@ -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}