论文信息 - On color-critical (P5, co-P5)-free graphs

On color-critical (P5, co-P5)-free graphs

Abstract 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 P 5 -free graphs is finite, but there is an infinite number of k -critical P 5 -free graphs for each k ≥ 5 . We show that the number of k -critical ( P 5 , P ¯ 5 ) -free graphs is finite for every fixed k . Our result implies the existence of a certifying algorithm for k -coloring ( P 5 , P ¯ 5 ) -free graphs.

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