Three-Coloring and List Three-Coloring of Graphs Without Induced Paths on Seven Vertices

Abstract

In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002. Our algorithm also solves the list-coloring version of the 3-coloring problem, where every vertex is assigned a list of colors that is a subset of {1,2,3}, and gives an explicit coloring if one exists.

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Correspondence to Flavia Bonomo.

Additional information

Partially supported by MathAmSud Project 13MATH–07, UBACyT Grant 20020130100808BA, CONICET PIP 112–201201–00450CO and ANPCyT PICT 2012–1324.

Partially supported by NSF grants IIS-1117631, DMS-1001091 and DMS-1265803.

Partially supported by MathAmSud Project 13MATH-07, Fondecyt grant 1140766, and Millenium Nucleus Information and Coordination in Networks.

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Bonomo, F., Chudnovsky, M., Maceli, P. et al. Three-Coloring and List Three-Coloring of Graphs Without Induced Paths on Seven Vertices. Combinatorica 38, 779–801 (2018). https://doi.org/10.1007/s00493-017-3553-8

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Mathematics Subject Classification (2000)

  • 05C15
  • 05C37
  • 05C85