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Partial Complementation of Graphs

Authors Fedor V. Fomin , Petr A. Golovach , Torstein J. F. Strømme , Dimitrios M. Thilikos

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Fedor V. Fomin
  • Department of Informatics, University of Bergen, Norway
Petr A. Golovach
  • Department of Informatics, University of Bergen, Norway
Torstein J. F. Strømme
  • Department of Informatics, University of Bergen, Norway
Dimitrios M. Thilikos
  • AlGCo project-team, LIRMM, Université de Montpellier, CNRS, France. , Department of Mathematics National and Kapodistrian University of Athens, Greece

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Fedor V. Fomin, Petr A. Golovach, Torstein J. F. Strømme, and Dimitrios M. Thilikos. Partial Complementation of Graphs. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 21:1-21:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


A partial complement of the graph G is a graph obtained from G by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph G and graph class G, is there a partial complement of G which is in G? We show that this problem can be solved in polynomial time for various choices of the graphs class G, such as bipartite, degenerate, or cographs. We complement these results by proving that the problem is NP-complete when G is the class of r-regular graphs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Graph algorithms analysis
  • Partial complementation
  • graph editing
  • graph classes


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