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 .
Graph burning runs on discrete time steps. The aim is to burn all the vertices in a given graph in the least number of time steps. This number 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 faster the spread. Optimal burning of general graphs is NP-Hard. There is a 3-approximation algorithm to burn general graphs where as better approximation factors are there for many sub classes. Here we study burning of grids; provide a lower bound for burning arbitrary grids and a 2-approximation algorithm for burning square grids. On the other hand, burning path forests, spider graphs, and trees with maximum degree three is already known to be NP-Complete. In this article we show burning problem to be NP-Complete on connected interval graphs, permutation graphs and several other geometric graph classes as corollaries .
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Computationally, graph burning is hard. It has already been proved that burning of
Optimal burning of general graphs is NP-Hard. There is a 3-approximation algorithm to burn general graphs where as better approximation factors are there for many sub classes. Here we study burning of grids; provide a lower bound for burning arbitrary grids and a 2-approximation algorithm for burning square grids. On the other hand, burning
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work we study graph burning on geometric graphs and show NP-completeness results on several sub classes. More precisely, we show
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NP-complete on interval graph, permutation graph and disk graph
NP-Complete on connected interval graphs, permutation graphs and several other geometric graph classes as corollaries