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Polynomial Cases for the Vertex Coloring Problem

2018; Springer Science+Business Media; Volume: 81; Issue: 3 Linguagem: Inglês

10.1007/s00453-018-0457-y

1432-0541

T. Karthick, Frédéric Maffray, Lucas Pastor,

Limits and Structures in Graph Theory

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.