Burning a graph is hard

Stéphane Bessy, Anthony Bonato, Jeannette Janssen, Dieter Rautenbach, Elham Roshanbin
2017 Discrete Applied Mathematics  
We introduce a new graph parameter called the burning number, inspired by contact processes on graphs such as graph bootstrap percolation, and graph searching paradigms such as Firefighter. The burning number measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We provide algorithmic results on the burning number, and prove the corresponding graph decision problem is NP-complete even when restricted to graph classes such as
more » ... nar graphs, disconnected graphs, or bipartite graphs.
doi:10.1016/j.dam.2017.07.016 fatcat:n5hpmiwmd5dxlhcqozii2gmo4m