The Graph Burning Conjecture is true for trees without degree-2 vertices

Abstract

Graph burning is a discrete time process which can be used to model the spread of social contagion. One is initially given a graph of unburned vertices. At each round (time step), one vertex is burned; unburned vertices with at least one burned neighbour from the previous round also becomes burned. The burning number of a graph is the fewest number of rounds required to burn the graph. It has been conjectured that for a graph on $n$ vertices, the burning number is at most $\lceil\sqrt{n}\rceil$. We show that the graph burning conjecture is true for trees without degree-2 vertices.