A CHARACTERIZATION OF ACYCLIC SWITCHING CLASSES OF GRAPHS USING FORBIDDEN SUBGRAPHS

Abstract. We characterize the switching classes that do not contain an acyclic graph. The characterization is by means of a set of forbidden graphs. We prove that in addition to switches of the cycles Cn for n ≥ 7 there are only finitely many such graphs in 24 switching classes, all having at most 9 vertices. We give a representative of each of the 24 switching classes. Key words. Graphs, switching class. Seidel switching, acyclic graphs, trees, forbidden graphs, critically cyclic graphs AMS subject classifications. 05 1. Introduction. Blue things are new, red things are replaced (by the blue if applicable) For a finite undirected graph G = (V, E) and a set σ ⊆ V, the switch of G by σ is defined as the graph G σ = (V, E ′), which is obtained from G by removing all edges between σ and its complement σ and adding as edges all nonedges between σ an