Graphs measure interactions between objects such as friendship links on Twitter,
transactions between Bitcoin users, and the flow of energy in a food chain. While graphs …

Graph burning is a deterministic, discrete-time process that models how influence or
contagion spreads in a graph. Associated to each graph is its burning number, which is a …

The burning number b (G) of a graph G is the smallest number of turns required to burn all
vertices of a graph if at every turn a new fire is started and existing fires spread to all …

The Burning Number Conjecture claims that for every connected graph $ G $ of order $ n, $
its burning number satisfies $ b (G)\le\lceil\sqrt {n}\rceil. $ While the conjecture remains …

The graph burning problem is an NP-hard combinatorial optimization problem that helps
quantify how vulnerable a graph is to contagion. This paper introduces three mathematical …

Graph burning is a process to determine the spreading of information in a graph. If a
sequence of vertices burns all the vertices of a graph by following the graph burning …

The burning number of a graph can be used to measure the spreading speed of contagion
in a network. The burning number conjecture is arguably the main unresolved conjecture …

Graph Burning asks, given a graph G=(V, E) and an integer k, whether there exists (b 0,⋯, bk-
1)∈ V k such that every vertex in G has distance at most i from some bi. This problem is …

Given a graph $ G $, the optimization version of the graph burning problem seeks for a
sequence of vertices, $(u_1, u_2,..., u_p)\in V (G)^ p $, with minimum $ p $ and such that …

The burning number of a graph $ G $ is the smallest number $ b $ such that the vertices of $
G $ can be covered by balls of radii $0, 1,\dots, b-1$. As computing the burning number of a …