Stefan A. Panait

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A graph is k-critical if it is k-chromatic but each of its proper induced subgraphs is (k− 1)colorable. It is known that the number of 4-critical P5-free graphs is finite, but there is an infinite number of k-critical P5-free graphs for each k ≥ 5. We show that the number of k-critical (P5, P5)-free graphs is finite for every fixed k. Our result implies the(More)
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