Vertex gluing preserves the bunkbed conjecture

Abstract

We prove that the bunkbed conjecture is preserved under gluing along a vertex. As a consequence, every minimal counterexample is 2-connected. More generally, for any class of graphs closed under taking 2-connected components, the study of the bunkbed conjecture reduces to the case of 2-connected graphs in that class. In particular, the conjecture holds for forests and block graphs.

10 pages, 2 figures, updated title, minor edits