Vertex-critical graphs in co-gem-free graphs

Iain Beaton, Ben Cameron

A graph $G$ is $k$-vertex-critical if $\chi (G)=k$ but $\chi (G-v)<k$ for all $v\in V(G)$ and $(G,H)$-free if it contains no induced subgraph isomorphic to $G$ or $H$. We show that there a…