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Combinatorica

, Volume 38, Issue 4, pp 779–801 | Cite as

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

  • Flavia Bonomo
  • Maria Chudnovsky
  • Peter Maceli
  • Oliver Schaudt
  • Maya Stein
  • Mingxian Zhong
Article

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.

Mathematics Subject Classification (2000)

05C15 05C37 05C85 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Flavia Bonomo
    • 1
  • Maria Chudnovsky
    • 2
  • Peter Maceli
    • 3
  • Oliver Schaudt
    • 4
  • Maya Stein
    • 5
  • Mingxian Zhong
    • 6
  1. 1.CONICET and Departamento de Computación, FCENUniversidad de Buenos AiresAiresArgentina
  2. 2.Princeton UniversityPrincetonUSA
  3. 3.Department of Mathematics and StatisticsCanisius CollegeBuffaloUSA
  4. 4.Institut für InformatikUniversität zu KälnKälnGermany
  5. 5.Departamento de Ingeniería MatemáticaUniversidad de ChileSantiagoChile
  6. 6.Columbia UniversityNew YorkUSA

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