Partial Complementation of Graphs

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 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