Complexity of the Cluster Vertex Deletion Problem on H-Free Graphs

Authors Hoang-Oanh Le, Van Bang Le

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Hoang-Oanh Le
  • Independent Researcher, Berlin, Germany
Van Bang Le
  • Institut für Informatik, Universität Rostock, Germany

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Hoang-Oanh Le and Van Bang Le. Complexity of the Cluster Vertex Deletion Problem on H-Free Graphs. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 68:1-68:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


The well-known Cluster Vertex Deletion problem (cluster-vd) asks for a given graph G and an integer k whether it is possible to delete at most k vertices of G such that the resulting graph is a cluster graph (a disjoint union of cliques). We give a complete characterization of graphs H for which cluster-vd on H-free graphs is polynomially solvable and for which it is NP-complete.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph theory
  • Mathematics of computing → Graph algorithms
  • Cluster vertex deletion
  • Vertex cover
  • Computational complexity
  • Complexity dichotomy


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