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Graphs and Combinatorics

, Volume 31, Issue 1, pp 73–90 | Cite as

Blockers for the Stability Number and the Chromatic Number

  • C. Bazgan
  • C. Bentz
  • C. Picouleau
  • B. Ries
Original Paper

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.

Keywords

Blocker Chromatic number Stability number Bipartitegraph Split graph Threshold graph 

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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.PSL, LAMSADE, CNRS UMR 7243Université Paris-DauphineParisFrance
  2. 2.Institut Universitaire de FranceParisFrance
  3. 3.CEDRIC-CNAMParisFrance

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