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.
@InProceedings{fomin_et_al:LIPIcs.SWAT.2018.21, author = {Fomin, Fedor V. and Golovach, Petr A. and Str{\o}mme, Torstein J. F. and Thilikos, Dimitrios M.}, title = {{Partial Complementation of Graphs}}, booktitle = {16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)}, pages = {21:1--21:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-068-2}, ISSN = {1868-8969}, year = {2018}, volume = {101}, editor = {Eppstein, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.21}, URN = {urn:nbn:de:0030-drops-88476}, doi = {10.4230/LIPIcs.SWAT.2018.21}, annote = {Keywords: Partial complementation, graph editing, graph classes} }
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