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Colouring square-free graphs without long induced paths.

Gaspers, Serge and Huang, Shenwei and Paulusma, Daniël (2019) 'Colouring square-free graphs without long induced paths.', Journal of computer and system sciences., 106 . pp. 60-79.


The complexity of Colouring is fully understood for H-free graphs, but there are still major complexity gaps if two induced subgraphs and are forbidden. Let be the s-vertex cycle and be the t-vertex path . We show that Colouring is polynomial-time solvable for and , 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. As a complementary result we prove that Colouring is NP-complete for and , which is the first hardness result on Colouring for -free graphs. Combining our new results with known results leads to an almost complete dichotomy for Colouring restricted to -free graphs.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:22 June 2019
Date deposited:02 July 2019
Date of first online publication:28 June 2019
Date first made open access:28 June 2020

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