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Colouring Square-Free Graphs without Long Induced Paths
[article]
2018
arXiv
pre-print
The complexity of Colouring is fully understood for H-free graphs, but there are still major complexity gaps if two induced subgraphs H_1 and H_2 are forbidden. Let H_1 be the s-vertex cycle C_s and H_2 be the t-vertex path P_t. We show that Colouring is polynomial-time solvable for s=4 and t≤ 6, strengthening several known results. Our main approach is to initiate a study into the boundedness of the clique-width of atoms (graphs with no clique cutset) of a hereditary graph class. We first show
arXiv:1805.08270v1
fatcat:alqgbles2ncihj3yahfe2w5zc4