Abstract
Given a graph G and an integer k, the Graph Burning problem asks whether the graph G can be burned in at most k rounds. Graph burning is a model for information spreading in a network, where we study how fast the information spreads in the network through its vertices. In each round, the fire is started at an unburned vertex, and fire spreads from every burned vertex to all its neighbors in the subsequent round burning all of them and so on. The minimum number of rounds required to burn the whole graph G is called the burning number of G. Graph Burning is NP-hard even for the union of disjoint paths. Moreover, Graph Burning is known to be W[1]-hard when parameterized by the burning number and para-NP-hard when parameterized by treewidth. In this paper, we prove the following results:
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