A graph is k-vertex-critical if \(\chi (G)=k\) but \(\chi (G-v)<k\) for all \(v\in V(G)\) . We construct new infinite families of k-vertex-critical \((P_5,C_5)\) -free graphs for all \(k\ge 6\) . Our construction generalises known constructions for 4-vertex-critical \(P_7\) -free graphs and 5-vertex-critical \(P_5\) -free graphs and is in contrast to the fact that there are only finitely many 5-vertex-critical \((P_5,C_5)\) -free graphs. In fact, our construction is even more well-structured, being \((2P_2,K_3+P_1,C_5)\) -free.
