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