Burning a graph is hard

Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We prove that the corresponding graph deci...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 232; pp. 73 - 87
Main Authors: Bessy, Stéphane, Bonato, Anthony, Janssen, Jeannette, Rautenbach, Dieter, Roshanbin, Elham
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 11.12.2017
Elsevier BV
Elsevier
Subjects:
3-partition
Algorithms
Approximation
Approximation algorithm
Burning rate
Computational complexity
Computer Science
Discrete Mathematics
Forests
Graph burning
Graphs
Mathematical analysis
Mathematics
NP-complete
Polynomial time algorithm
Polynomials
3-partition
NP-complete
Graph burning
Polynomial time algorithm
Approximation algorithm
Computational complexity
NP-complete3-partition
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We prove that the corresponding graph decision problem is NP-complete when restricted to acyclic graphs with maximum degree three, spider graphs and path-forests. We provide polynomial time algorithms for finding the burning number of spider graphs and path-forests if the number of arms and components, respectively, are fixed. Finally, we describe a polynomial time approximation algorithm with approximation factor 3 for general graphs.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2017.07.016