Note on Choudum's "chromatic bounds for a class of graphs"
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If a graph G has no induced subgraph isomorphic to K1,3′K5-e, or a third graph that can be selected from two specific graphs, then the chromatic number of G is either d or d + 1, where d is the maximum order of a clique in G.
[1] S. A. Choudum. CHROMATIC BOUNDS FOR A CLASS OF GRAPHS , 1977 .