Conference paper (in proceedings)

Using Edge Contractions and Vertex Deletions to Reduce the Independence Number and the Clique Number


  • 29.05.2022
Published in:
  • Combinatorial Algorithms / Bazgan, Cristina ; Fernau, Henning. - Springer International Publishing. - 2022, p. 412-424
English We consider the following problem: for a given graph G and two integers k and d, can we apply a fixed graph operation at most k times in order to reduce a given graph parameter π by at least d? We show that this problem is NP-hard when the parameter is the independence number and the graph operation is vertex deletion or edge contraction, even for fixed d = 1 and when restricted to chordal graphs. We also give a polynomial time algorithm for bipartite graphs when the operation is edge contraction, the parameter is the independence number and d is fixed. Further, we complete the complexity dichotomy on H-free graphs when the parameter is the clique number and the operation is edge contraction by showing that this problem is NP-hard in (C3 +P1)-free graphs even for fixed d = 1. Our results answer several open questions stated in [Diner et al., Theoretical Computer Science, 746, p. 49-72 (2012)].
Faculté des sciences économiques et sociales et du management
Département d'informatique
  • English
Computer science and technology
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