Let us return to the analysis of our algorithm.
-\thmn{MST on minor-closed classes, Mare\v{s} \cite{mm:mst}}\id{mstmcc}%
+\thmn{MST on minor-closed classes, Tarjan \cite{tarjan:dsna}}\id{mstmcc}%
For any fixed non-trivial minor-closed class~$\cal C$ of graphs, the Contractive Bor\o{u}vka's
algorithm (\ref{contbor}) finds the MST of any graph of this class in time
$\O(n)$. (The constant hidden in the~$\O$ depends on the class.)
\figure{hexangle.eps}{\epsfxsize}{The construction from Remark~\ref{hexa}}
\rem
-The observation in~Theorem~\ref{mstmcc} was also independently made by Gustedt \cite{gustedt:parallel},
-who studied a~parallel version of the Contractive Bor\o{u}vka's algorithm applied
+The observation in~Theorem~\ref{mstmcc} was also used by Gustedt \cite{gustedt:parallel},
+to construct parallel version of the Contractive Bor\o{u}vka's algorithm applied
to minor-closed classes.
\rem