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

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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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Author information

Authors and Affiliations

  1. CONICET and Departamento de Computación, FCEN, Universidad de Buenos Aires, Aires, Argentina

    Flavia Bonomo

  2. Princeton University, Princeton, NJ, 08544, USA

    Maria Chudnovsky

  3. Department of Mathematics and Statistics, Canisius College, Buffalo, NY, 14208, USA

    Peter Maceli

  4. Institut für Informatik, Universität zu Käln, Käln, Germany

    Oliver Schaudt

  5. Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile

    Maya Stein

  6. Columbia University, New York, NY, 10027, USA

    Mingxian Zhong

Authors
  1. Flavia Bonomo
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  2. Maria Chudnovsky
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  3. Peter Maceli
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  4. Oliver Schaudt
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  5. Maya Stein
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  6. Mingxian Zhong
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Corresponding author

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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  • DOI: https://doi.org/10.1007/s00493-017-3553-8

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