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Simple Max-Cut for Split-Indifference Graphs and Graphs with Few P 4’s

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Experimental and Efficient Algorithms (WEA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3059))

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Abstract

The simple max-cut problem is as follows: given a graph, find a partition of its vertex set into two disjoint sets, such that the number of edges having one endpoint in each set is as large as possible. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. The simple max-cut decision problem is known to be NP-complete for split graphs. An indifference graph is the intersection graph of a set of unit intervals of the real line. We show that the simple max-cut problem can be solved in linear time for a graph that is both split and indifference. Moreover, we also show that for each constant q, the simple max-cut problem can be solved in polynomial time for (q,q-4)-graphs. These are graphs for which no set of at most q vertices induces more than q-4 distinct P 4’s.

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Author information

Authors and Affiliations

  1. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970, Rio de Janeiro, Brazil

    Celina M. H. de Figueiredo

  3. Departamento de Matemática, Universidad Nacional de La Plata, C. C. 172 (1900), La Plata, Argentina

    Marisa Gutierrez

  4.  ,  

    Ton Kloks

  5. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Germany

    Rolf Niedermeier

Authors
  1. Hans L. Bodlaender
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  2. Celina M. H. de Figueiredo
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  3. Marisa Gutierrez
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  4. Ton Kloks
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  5. Rolf Niedermeier
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Universidade Federal Fluminense, Rua Passo da Pátria, 156, Bloco E, RJ 24210-240, Niterói, Brazil

    Celso C. Ribeiro

  2. Departamento de Ciência da Computação, Universidade Federal Fluminense, Niterói, RJ, Brazil

    Simone L. Martins

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© 2004 Springer-Verlag Berlin Heidelberg

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Bodlaender, H.L., de Figueiredo, C.M.H., Gutierrez, M., Kloks, T., Niedermeier, R. (2004). Simple Max-Cut for Split-Indifference Graphs and Graphs with Few P 4’s. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_7

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  • DOI: https://doi.org/10.1007/978-3-540-24838-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22067-1

  • Online ISBN: 978-3-540-24838-5

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