NP-completeness Results for Graph Burning on Geometric Graphs
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Graph burning runs on discrete time steps. The aim of the graph burning problem is to burn all the vertices in a given graph in the least amount of time steps. The least number of required time steps is known to be the burning number of the graph. The spread of social influence, an alarm, or a social contagion can be modeled using graph burning. The less the burning number, the quick the spread. Computationally, graph burning is hard. It has already been proved that burning of path forests, spider graphs, and trees with maximum degree three are NP-Complete. In this work we study graph burning on geometric graphs and show NP-completeness results on several sub classes. More precisely, we show burning problem to be NP-complete on interval graph, permutation graph and disk graph.
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