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
