Abstract
Graph burning is a deterministic discrete time graph process that can be interpreted as a model for the spread of influence in social networks. The burning number b(G) of a graph G is the minimum number of steps in a graph burning process for G. Bonato et al. (2014) conjectured that b(G)≤⌈n⌉ for any connected graph G of order n. In this paper, we confirm this conjecture for caterpillars. We also determine the burning numbers of caterpillars with at most two stems and a subclass of the class of caterpillars all of whose spine vertices are stems.
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