Four-coloring $P_6$-free graphs. I. Extending an excellent precoloring

12 Jul 2018 Chudnovsky Maria Spirkl Sophie Zhong Mingxian

This is the first paper in a series whose goal is to give a polynomial time algorithm for the $4$-coloring problem and the $4$-precoloring extension problem restricted to the class of graphs with no induced six-vertex path, thus proving a conjecture of Huang. Combined with previously known results this completes the classification of the complexity of the $4$-coloring problem for graphs with a connected forbidden induced subgraph... (read more)

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