Burning a Graph is Hard
Combinatorics
2015-11-24 v1
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.
Keywords
Cite
@article{arxiv.1511.06774,
title = {Burning a Graph is Hard},
author = {Anthony Bonato and Jeannette Janssen and Elham Roshanbin},
journal= {arXiv preprint arXiv:1511.06774},
year = {2015}
}
Comments
20 Pages, 4 figures, presented at GRASTA-MAC 2015 (October 19-23rd, 2015, Montr\'eal, Canada)