Abstract
We prove that if G is a vertex-critical graph with χ(G)≥Δ(G)+1−p≥4 for some p∈N and ω(H(G))≤χ(G)+1p+1−2, then G=Kχ(G) or G=O5. Here H(G) is the subgraph of G induced on the vertices of degree at least χ(G). This simplifies the proofs and improves the results in the paper of Kostochka, Rabern and Stiebitz (2012) [8].
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