Δ-Critical graphs with small high vertex cliques

We prove that Kχ(G) is the only vertex critical graph G with χ(G)⩾Δ(G)⩾6 and . Here H(G) is the subgraph of G induced on the vertices of degree at least χ(G). Setting ω(H(G))=1 proves a conjecture of Kierstead and Kostochka.