Abstract
If G is a graph which induces neither K 1,3 nor K 5− e and if Δ( G)⩽2 ω( G)−5, then χ( G) = ω( G). Conversely, for each k ⩾ 4 there is a graph G which induces neither K 1,3 nor K 5− e such that ω( G) = k, Δ( G) = 2 k − 3 and χ( G) = k + 1.
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