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International Conference on Algorithms and Complexity

CIAC 2015: Algorithms and Complexity pp 194–207Cite as

Contraction Blockers for Graphs with Forbidden Induced Paths

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9079)

Abstract

We consider the following problem: can a certain graph parameter of some given graph be reduced by at least \(d\) for some integer \(d\) via at most \(k\) edge contractions for some given integer \(k\)? We examine three graph parameters: the chromatic number, clique number and independence number. For each of these graph parameters we show that, when \(d\) is part of the input, this problem is polynomial-time solvable on \(P_4\)-free graphs and NP-complete as well as W[1]-hard, with parameter \(d\), for split graphs. As split graphs form a subclass of \(P_5\)-free graphs, both results together give a complete complexity classification for \(P_\ell \)-free graphs. The W[1]-hardness result implies that it is unlikely that the problem is fixed-parameter tractable for split graphs with parameter \(d\). But we do show, on the positive side, that the problem is polynomial-time solvable, for each parameter, on split graphs if \(d\) is fixed, i.e., not part of the input. We also initiate a study into other subclasses of perfect graphs, namely cobipartite graphs and interval graphs.

Keywords

  • Chromatic Number
  • Interval Graph
  • Chordal Graph
  • Graph Class
  • Perfect Graph

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Öznur Yaşar Diner—Supported partially by Marie Curie International Reintegration Grant PIRG07/GA/2010/268322.

Daniël Paulusma—Supported by EPSRC EP/K025090/1.

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Authors and Affiliations

  1. Computer Engineering Department, Kadir Has University, Istanbul, Turkey

    Öznur Yaşar Diner

  2. School of Engineering and Computing Sciences, Durham University, Durham, UK

    Daniël Paulusma

  3. Laboratoire CEDRIC, CNAM, Paris, France

    Christophe Picouleau

  4. PSL, Université Paris-Dauphine and CNRS, LAMSADE UMR 7243, Paris, France

    Bernard Ries

Authors
  1. Öznur Yaşar Diner
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  2. Daniël Paulusma
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  3. Christophe Picouleau
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  4. Bernard Ries
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Corresponding author

Correspondence to Öznur Yaşar Diner .

Editor information

Editors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France

    Vangelis Th. Paschos

  2. Inst. of Theoretical Computer Science, ETH Zürich, Zürich, Switzerland

    Peter Widmayer

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Diner, Ö.Y., Paulusma, D., Picouleau, C., Ries, B. (2015). Contraction Blockers for Graphs with Forbidden Induced Paths. In: Paschos, V., Widmayer, P. (eds) Algorithms and Complexity. CIAC 2015. Lecture Notes in Computer Science(), vol 9079. Springer, Cham. https://doi.org/10.1007/978-3-319-18173-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-18173-8_14

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