NP-Completeness Results for Graph Burning on Geometric Graphs
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.
Keywords
Cite
@article{arxiv.2003.07746,
title = {NP-Completeness Results for Graph Burning on Geometric Graphs},
author = {Arya Tanmay Gupta and Swapnil A. Lokhande and Kaushik Mondal},
journal= {arXiv preprint arXiv:2003.07746},
year = {2021}
}
Comments
17 pages, 5 figures