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arXiv · 2312.13972

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

Yukihiro Murakami
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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.

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Yukihiro Murakami. 2023-12-21. The Graph Burning Conjecture is true for trees without degree-2 vertices. https://arxiv.org/abs/2312.13972

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