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On Vertex Coloring Without Monochromatic Triangles

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Computer Science – Theory and Applications (CSR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10846))

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Abstract

We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of classic and parametrized algorithms. Several computational complexity results are also presented, which improve on the previous results found in the literature. We propose the new structural parameter for undirected, simple graphs – the triangle-free chromatic number \(\chi _3\). We bound \(\chi _3\) by other known structural parameters. We also present two classes of graphs with interesting coloring properties, that play pivotal role in proving useful observations about our problem.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Joliot-Curie 15, 50-383, Wrocław, Poland

    Michał Karpiński & Krzysztof Piecuch

Authors
  1. Michał Karpiński
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  2. Krzysztof Piecuch
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Correspondence to Michał Karpiński .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Steklov Mathematical Institute, Moscow, Russia

    Vladimir V. Podolskii

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Karpiński, M., Piecuch, K. (2018). On Vertex Coloring Without Monochromatic Triangles. In: Fomin, F., Podolskii, V. (eds) Computer Science – Theory and Applications. CSR 2018. Lecture Notes in Computer Science(), vol 10846. Springer, Cham. https://doi.org/10.1007/978-3-319-90530-3_19

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  • DOI: https://doi.org/10.1007/978-3-319-90530-3_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90529-7

  • Online ISBN: 978-3-319-90530-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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