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Upper Bound on the Burning Number of Graphs
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The article was published on 2017-01-01 and is currently open access. It has received 24 citations till now. The article focuses on the topics: Upper and lower bounds.read more
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Book ChapterDOI
Approximation Algorithms for Graph Burning
Anthony Bonato,Shahin Kamali +1 more
TL;DR: Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph, to find a schedule that minimizes the number of rounds to burn graph.
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Bounds on the burning numbers of spiders and path-forests
Anthony Bonato,Thomas Lidbetter +1 more
TL;DR: The conjecture that the burning number of a connected graph of order $n$ is at most $\lceil \sqrt{n} \rceil$ is proved for spider graphs, which are trees with exactly one vertex of degree at least 3, which is the conjectured bound for graph burning.
Journal ArticleDOI
On the Burning Number of Generalized Petersen Graphs
TL;DR: In this article, the authors studied the burning number of the generalized Petersen graph P(n, k) for any fixed positive integer k and gave tight bounds for b(P(k, n, 1)) and b(p n, k, 2)).
Journal ArticleDOI
Burning number of theta graphs
TL;DR: It is shown that the burning number of any theta graph of order n = q 2 + r with 1 ≤ r ≤ 2q + 1 is either q or q + 1, and all theta graphs that have burning number q orQ + 1 are characterized.
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Burning graphs - a probabilistic perspective
TL;DR: In this paper, the original burning number is revisited and analyzed for binomial random graphs G(n,p), random geometric graphs, and the Cartesian product of paths, and new variants of the burning number are introduced in which a burning sequence of vertices is selected according to some probabilistic rules.
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Book
Graph theory 1736-1936
TL;DR: The four-colour problem has been studied in the context of graph theory since 1936 as discussed by the authors, with a focus on the factorization of graphs and its application to the problem of graph factorization.
The Firefighter Problem: a survey of results, directions and questions.
Stephen Finbow,Gary MacGillivray +1 more
TL;DR: The paper concludes with a collection of 26 open problems and possible research projects for The Firefighter Problem, which has attracted considerable attention since being introduced in 1995.
Journal ArticleDOI
The firefighter problem for graphs of maximum degree three
TL;DR: It is shown that the firefighter problem is NP-complete for trees ofmaximum degree three, but in P for graphs of maximum degree three if the fire breaks out at a vertex of degree at most two.
Book ChapterDOI
Burning a Graph as a Model of Social Contagion
TL;DR: A new graph parameter called the burning number is introduced, inspired by contact processes on graphs such as graph bootstrap percolation, and graph searching paradigms such as Firefighter, which measures the speed of the spread of contagion in a graph.
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Burning a Graph is Hard
TL;DR: It is proved that the corresponding graph decision problem is \textbf{NP}-complete when restricted to acyclic graphs with maximum degree three, spider graphs and path-forests if the number of arms and components, respectively, are fixed.