6 research outputs found
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 decision
problem is \textbf{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.Comment: 20 Pages, 4 figures, presented at GRASTA-MAC 2015 (October 19-23rd,
2015, Montr\'eal, Canada
BURNING NUMBER OF GRAPH PRODUCTS
International audienceGraph burning is a deterministic discrete time graph process that can be interpreted as a model for the spread of influence in social networks. The burning number of a graph is the minimum number of steps in a graph burning process for that graph. In this paper, we consider the burning number of graph products. We find some general bounds on the burning number of the Cartesian product and the strong product of graphs. In particular, we determine the asymptotic value of the burning number of hypercube graphs and we present a conjecture for its exact value. We also find the asymptotic value of the burning number of the strong grids, and using that we obtain a lower bound on the burning number of the strong product of graphs in terms of their diameters. Finally, we consider the burning number of the lexicographic product of graphs and we find a characterization for that