DeepAI AI Chat
Log In Sign Up

NP-completeness Results for Graph Burning on Geometric Graphs

by   Arya Tanmay Gupta, et al.

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.


page 1

page 2

page 3

page 4


Burning Geometric Graphs

A procedure called graph burning was introduced to facilitate the modell...

On the Burning Number of p-Caterpillars

The burning number is a recently introduced graph parameter indicating t...

Making Life More Confusing for Firefighters

It is well known that fighting a fire is a hard task. The Firefighter pr...

Proving the NP-completeness of optimal moral graph triangulation

Moral graphs were introduced in the 1980s as an intermediate step when t...

Path Puzzles: Discrete Tomography with a Path Constraint is Hard

We prove that path puzzles with complete row and column information--or ...

On NP-completeness of the cell formation problem

In the current paper we provide a proof of NP-completeness for the CFP p...

Alternating Automatic Register Machines

This paper introduces and studies a new model of computation called an A...