Abstract
The computational complexity of the Vertex Coloring problem is known for all hereditary classes of graphs defined by forbidding two connected five-vertex induced subgraphs, except for seven cases. We prove the polynomial-time solvability of four of these problems: for (\(P_5\), dart)-free graphs, (\(P_5\), banner)-free graphs, (\(P_5\), bull)-free graphs, and (fork, bull)-free graphs.
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Acknowledgements
The first author would like to thank Mathew C. Francis for fruitful discussions. The second and third authors are supported by ANR Grant ANR-13-BS02-0007-STINT.
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Karthick, T., Maffray, F. & Pastor, L. Polynomial Cases for the Vertex Coloring Problem. Algorithmica 81, 1053–1074 (2019). https://doi.org/10.1007/s00453-018-0457-y
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DOI: https://doi.org/10.1007/s00453-018-0457-y