On Subgraph Complementation to H-free Graphs

For a class $$\mathcal {G}$$ of graphs, the problem Subgraph Complement to asks whether one can find subset S vertices input graph G such that complementing subgraph induced by in results . We investigate complexity when is H-free for H being complete graph, star, path, or cycle. obtain following results: Further, we prove these hard problems do not admit subexponential-time algorithms (algorithms running time $$2^{o(\mid V(G)\mid )}$$ ), assuming Exponential Time Hypothesis. show on also true $$\overline{\mathcal {G}}$$ complement graphs Therefore, each above mentioned valid $$\overline{H}$$ -free graphs. It noteworthy our generalize two main results, namely, triangle-free and d-degenerate resolves open question due Fomin et al. (Algorithmica, 2020).