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Reducing the Clique and Chromatic Number via Edge Contractions and Vertex Deletions

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Combinatorial Optimization (ISCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

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Abstract

We consider the following problem: can a certain graph parameter of some given graph G be reduced by at least d, for some integer d, via at most k graph operations from some specified set S, for some given integer k? As graph parameters we take the chromatic number and the clique number. We let the set S consist of either an edge contraction or a vertex deletion. As all these problems are NP-complete for general graphs even if d is fixed, we restrict the input graph G to some special graph class. We continue a line of research that considers these problems for subclasses of perfect graphs, but our main results are full classifications, from a computational complexity point of view, for graph classes characterized by forbidding a single induced connected subgraph H.

D. Paulusma—Author supported by EPSRC (EP/K025090/1).

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Notes

  1. 1.

    We can modify the gadgets for proving NP-completeness for the case \(d=1\) in a straightforward way to obtain NP-completeness for every constant \(d\ge 2\). A similar remark holds for other theorems. Details will be given in the journal version.

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Author information

Authors and Affiliations

  1. Durham University, Durham, UK

    Daniël Paulusma

  2. CNAM, Laboratoire CEDRIC, Paris, France

    Christophe Picouleau

  3. University of Fribourg, Fribourg, Switzerland

    Bernard Ries

Authors
  1. Daniël Paulusma
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  2. Christophe Picouleau
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  3. Bernard Ries
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Corresponding author

Correspondence to Christophe Picouleau .

Editor information

Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

  3. LAMSADE, Université Paris-Dauphine , Paris , France

    A. Ridha Mahjoub

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Paulusma, D., Picouleau, C., Ries, B. (2016). Reducing the Clique and Chromatic Number via Edge Contractions and Vertex Deletions. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_4

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

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