Four-coloring P6-free graphs. I. Extending an excellent precoloring.
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Date
2024
Authors
Chudnovsky, Maria
Spirkl, Sophie
Zhong, Mingxian
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics
Abstract
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. In this paper we give a polynomial-time algorithm that determines if a special kind of precoloring of a P6-free graph has a precoloring extension, and constructs such an extension if one exists. Combined with the main result of the second paper of the series, this gives a complete solution to the problem
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Keywords
coloring, induced subgraph, algorithm, path