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arXiv · 2003.07746

NP-Completeness Results for Graph Burning on Geometric Graphs

Arya Tanmay Gupta·Swapnil A. Lokhande·Kaushik Mondal
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Abstract

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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Arya Tanmay Gupta, Swapnil A. Lokhande, Kaushik Mondal. 2020-10-24. NP-Completeness Results for Graph Burning on Geometric Graphs. https://doi.org/10.1007/978-3-030-67899-9_6

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