几何图烧图的NP-完全性结果
NP-Completeness Results for Graph Burning on Geometric Graphs
摘要：
图形燃烧在离散时间步长上运行。其目标是在最少的时间步长内燃烧给定图中的所有顶点。这个数就是图的燃烧数。社会影响力的传播、警报或社会传染可以使用图形燃烧来建模。燃烧的数字越少，传播的速度越快。一般图的最优燃烧是NP-Hard问题。有一个3-近似算法燃烧一般的图形，其中作为更好的近似因子有许多子类。在这里，我们研究燃烧的网格，提供了一个下限燃烧任意网格和2-近似算法燃烧的正方形网格。另一方面，燃烧路径森林、蜘蛛图和最大度为3的树都是NP完全的。在这篇文章中，我们证明燃烧问题是NP-完全的连通区间图，置换图和其他几个几何图类作为推论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
