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Blockers for the Stability Number and the Chromatic Number

Graphs and Combinatorics volume 31, pages 73–90 (2015)Cite this article

Abstract

Given an undirected graph G = (V, E) and two positive integers k and d, we are interested in finding a set of edges (resp. non-edges) of size at most k to delete (resp. to add) in such a way that the chromatic number (resp. stability number) in the resulting graph will decrease by at least d compared to the original graph. We investigate these two problems in various classes of graphs (split graphs, threshold graphs, bipartite graphs and their complements) and determine their computational complexity. In some of the polynomial-time solvable cases, we also give a structural description of a solution.

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Authors and Affiliations

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

    C. Bazgan & B. Ries

  2. Institut Universitaire de France, Paris, France

    C. Bazgan

  3. CEDRIC-CNAM, Paris, France

    C. Bentz & C. Picouleau

Authors
  1. C. Bazgan
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  2. C. Bentz
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  3. C. Picouleau
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  4. B. Ries
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Correspondence to C. Picouleau.

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Bazgan, C., Bentz, C., Picouleau, C. et al. Blockers for the Stability Number and the Chromatic Number. Graphs and Combinatorics 31, 73–90 (2015). https://doi.org/10.1007/s00373-013-1380-2

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  • DOI: https://doi.org/10.1007/s00373-013-1380-2

Keywords

  • Blocker
  • Chromatic number
  • Stability number
  • Bipartitegraph
  • Split graph
  • Threshold graph