Complexity of hypergraph coloring and Seidel's switching

Abstract

Seidel's switching of a vertex in a given graph results in making the vertex adjacent to precisely those vertices it was nonadjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching equivalent if one can be transformed into the other one by a sequence of Seidel's switchings. We consider the computational complexity of deciding if an input graph can be switched into a graph having a desired graph property. Among other results we show that switching to a regular graph is NP-complete. The proof is based on an NP-complete variant of hypergraph bicoloring that we find interesting in its own. © Springer-Verlag Berlin Heidelberg 2003.