The Graph Burning Conjecture is true for trees without degree-2 vertices
arxiv(2023)
摘要
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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