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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2010: Graph Theoretic Concepts in Computer Science pp 15–26Cite as

max-cut and Containment Relations in Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6410))

Abstract

We study max-cut in classes of graphs defined by forbidding a single graph as a subgraph, induced subgraph, or minor. For the first two containment relations, we prove dichotomy theorems. For the minor order, we show how to solve max-cut in polynomial time for the class obtained by forbidding a graph with crossing number at most one (this generalizes a known result for K 5-minor-free graphs) and identify an open problem which is the missing case for a dichotomy theorem.

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Authors and Affiliations

  1. Département d’Informatique, Université Libre de Bruxelles, Belgium

    Marcin Kamiński

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  1. Marcin Kamiński
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Editors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistimioupolis, GR-15784, Athens, Greece

    Dimitrios M. Thilikos

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Kamiński, M. (2010). max-cut and Containment Relations in Graphs. In: Thilikos, D.M. (eds) Graph Theoretic Concepts in Computer Science. WG 2010. Lecture Notes in Computer Science, vol 6410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16926-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-16926-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16925-0

  • Online ISBN: 978-3-642-16926-7

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