diff --git a/papers/even_level_graph_generators/paper.pdf b/papers/even_level_graph_generators/paper.pdf index 832acb8..f78ab08 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 30dffee..8075a05 100644 --- a/papers/even_level_graph_generators/paper.tex +++ b/papers/even_level_graph_generators/paper.tex @@ -405,7 +405,26 @@ classes: two are Even Level Graphs outright, and the other four are bridge-derived level graphs. The bridge-switch restriction is what made the search tractable -- it both shrinks the orbit and guarantees validity, so any Even Level Graph located in a backward orbit is an -immediate witness. +immediate witness. Table~\ref{tab:n21} records the outcome for each dual. + +\begin{table}[ht] +\centering +\begin{tabular}{cccc} +dual & intertwining tree & Even Level Graph source & bridge switches to ELG \\\hline +$0$ & no & -- & $3$ \\ +$1$ & no & $10$ & $0$ \\ +$2$ & no & $9$ & $0$ \\ +$3$ & no & -- & $1$ \\ +$4$ & no & -- & $2$ \\ +$5$ & no & -- & $4$ \\ +\end{tabular} +\caption{The six Holton--McKay duals at $n = 21$, the first triangulations +that are not intertwining trees. Each is a bridge-derived level graph: +duals $1$ and $2$ are Even Level Graphs outright (zero switches), and the +remaining four reach an Even Level Graph in $1$--$4$ bridge switches. All +witnesses are step-verified.} +\label{tab:n21} +\end{table} \begin{thebibliography}{9}