The Burning Number Conjecture is True for Trees without Degree-2 Vertices
Yukihiro Murakami (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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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 ⌈n⌉. We show that the graph burning conjecture is true for trees without degree-2 vertices.
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