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arXiv · 1511.06774

Burning a Graph is Hard

Anthony Bonato·Jeannette Janssen·Elham Roshanbin
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Abstract

Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We prove that the corresponding graph decision problem is \textbf{NP}-complete when restricted to acyclic graphs with maximum degree three, spider graphs and path-forests. We provide polynomial time algorithms for finding the burning number of spider graphs and path-forests if the number of arms and components, respectively, are fixed.

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Anthony Bonato, Jeannette Janssen, Elham Roshanbin. 2015-11-20. Burning a Graph is Hard. https://arxiv.org/abs/1511.06774

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