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- W4212817891 abstract "There has been recently keen interest in finding polynomial-time algorithms for the VERTEX COLORING problem for graphs G that are F -free for a given set F of graphs. If L is a set of four-vertex graphs, then the complexity of VERTEX COLORING for L -free graphs is known with three exceptions: L 1 = {claw, 4 K 1 }, L 2 = {claw, 4 K 1 , co-diamond}, and L 3 = { 4 K 1 , C 4 }. In this paper, we study a problem arising from the class L 3 . A hole is an induced cycle with at least four vertices. A hole-twin is the graph obtained from a hole by adding a vertex that forms true twins with some vertex of the hole. A 5-wheel is the graph obtained from a C 5 by adding a vertex that is adjacent to all vertices of the C 5 . We prove that a ( 4 K 1 , hole-twin, 5-wheel)-free graph is perfect or has bounded clique width. As consequence we obtain a polynomial time algorithm for VERTEX COLORING for ( 4 K 1 , hole-twin, 5-wheel)-free graphs." @default.
- W4212817891 created "2022-02-24" @default.
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- W4212817891 date "2022-05-01" @default.
- W4212817891 modified "2023-09-26" @default.
- W4212817891 title "Vertex coloring (4K1, hole-twin, 5-wheel)-free graphs" @default.
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- W4212817891 doi "https://doi.org/10.1016/j.tcs.2022.02.009" @default.
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