Blockers for the stability number and the chromatic number

Cristina Bazgan (1) , Cédric Bentz (2) , Christophe Picouleau (3) , Bernard Ries (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
3 CEDRIC - Centre d'études et de recherche en informatique et communications

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, (complement of) bipartite graphs) and determine their computational complexity. In some of the polynomial-time solvable cases, we also give a structural description of a solution.

Mots clés: Threshold graph; split graph; stability number; chromatic number; blocker; bipartite graph

Domaines: Informatique [cs]; Complexité [cs.CC]

Cristina Bazgan, Cédric Bentz, Christophe Picouleau, Bernard Ries. Blockers for the stability number and the chromatic number. Graphs and Combinatorics, 2015, 31 (1), pp.73-90. ⟨10.1007/s00373-013-1380-2⟩. ⟨hal-01505546⟩