Partial complementation of graphs

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

doi:10.1007/s00453-020-00677-8

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arXiv · 1804.10920

Partial complementation of graphs

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

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Abstract

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 $\mathcal{G}$, is there a partial complement of $G$ which is in $\mathcal{G}$? We show that this problem can be solved in polynomial time for various choices of the graphs class $\mathcal{G}$, such as bipartite, degenerate, or cographs. We complement these results by proving that the problem is NP-complete when $\mathcal{G}$ is the class of $r$-regular graphs.

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BibTeX RIS

Fedor V. Fomin, Petr A. Golovach, Torstein J. F. Strømme, Dimitrios M. Thilikos. 2018-04-29. Partial complementation of graphs. https://doi.org/10.1007/s00453-020-00677-8

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