Remove source check count from table

papers/coloring_nested_tire_graphs/paper.tex

@@ -1348,27 +1348,27 @@ with the level-cycle three-colour restriction with respect to $S$.
 \subsection*{Enumeration for small $n$}
 
 We exhaustively enumerated all plane triangulation isomorphism classes with
-$4 \leq n \leq 12$ vertices and, for each graph, searched the vertex sources
-in order until a witness colouring was found or every source had been tested.
+$4 \leq n \leq 12$ vertices and searched the vertex sources for each graph.
 No counterexample to Conjecture~\ref{conj:level-cycle-three-colour} appeared
 in this range.  Table~\ref{tab:level-cycle-three-colour-counts} records the
-size of the search space and the amount of source-search work required.
+size of the search space and the number of triangulations that admit a
+witness.
 
 \begin{table}[ht]
 \centering
 \small
 \setlength{\tabcolsep}{4pt}
-\begin{tabular}{cccc}
-$n$ & triangulations & with witness & source checks \\\hline
-$4$  & $1$    & $1$    & $1$ \\
-$5$  & $1$    & $1$    & $1$ \\
-$6$  & $2$    & $2$    & $2$ \\
-$7$  & $5$    & $5$    & $5$ \\
-$8$  & $14$   & $14$   & $14$ \\
-$9$  & $50$   & $50$   & $50$ \\
-$10$ & $233$  & $233$  & $237$ \\
-$11$ & $1249$ & $1249$ & $1296$ \\
-$12$ & $7595$ & $7595$ & $8069$ \\
+\begin{tabular}{ccc}
+$n$ & triangulations & with witness \\\hline
+$4$  & $1$    & $1$ \\
+$5$  & $1$    & $1$ \\
+$6$  & $2$    & $2$ \\
+$7$  & $5$    & $5$ \\
+$8$  & $14$   & $14$ \\
+$9$  & $50$   & $50$ \\
+$10$ & $233$  & $233$ \\
+$11$ & $1249$ & $1249$ \\
+$12$ & $7595$ & $7595$ \\
 \end{tabular}
 \caption{Exhaustive vertex-source search for the level-cycle three-colour conjecture on all triangulation isomorphism classes with $4 \leq n \leq 12$.  Every triangulation in this range admits at least one vertex source witnessing the conjecture.}
 \label{tab:level-cycle-three-colour-counts}