The bunkbed conjecture remains true when gluing along a vertex

TL;DR

This paper proves that the bunkbed conjecture holds when graphs are glued along a vertex, confirming its validity for forests and establishing that any minimal counterexample must be 2-connected.

Contribution

The paper extends the bunkbed conjecture's validity to graphs glued along a vertex and identifies structural properties of potential counterexamples.

Findings

Bunkbed conjecture remains true when gluing along a vertex.

Bunkbed conjecture is true for forests.

Minimal counterexamples are 2-connected.

Abstract

We show that the bunkbed conjecture remains true when gluing along a vertex. As immediate corollaries, we obtain that the bunkbed conjecture is true for forests and that a minimal counterexample to the bunkbed conjecture is 2-connected.