Lucke, Felicia Mann, Felix 2022-05-29 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)]. application/pdf https://folia.unifr.ch/global/documents/322641 https://folia.unifr.ch/documents/322641/files/final_version_0.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-031-06678-8_30 info:eu-repo/semantics/altIdentifier/issn/0302-9743 info:eu-repo/semantics/altIdentifier/isbn/9783031066771 info:eu-repo/semantics/openAccess Rights reserved Combinatorial Algorithms / Bazgan, Cristina ; Fernau, Henning. - Springer International Publishing. - 2022, p. 412-424 Blocker problems Edge contraction Vertex deletion Independence number Clique number info:eu-repo/classification/udc/004 Using Edge Contractions and Vertex Deletions to Reduce the Independence Number and the Clique Number http://purl.org/coar/resource_type/c_5794