$\Delta$-critical graphs with a vertex of degree 2
$\Delta$-critical graphs with a vertex of degree 2
Let $G$ be a simple graph with maximum degree $\Delta$. A classic result of Vizing shows that $\chi'(G)$, the chromatic index of $G$, is either $\Delta$ or $\Delta+1$. We say $G$ is of \emph{Class 1} if $\chi'(G)=\Delta$, and is of \emph{Class 2} otherwise. A graph $G$ is \emph{$\Delta$-critical} if $\chi'(G)=\Delta+1$ …