Burning a graph is hard

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 planar graphs, disconnected graphs, or bipartite graphs.