Algorithms and Models for the Web Graph

The burning number b(G) of a graph G was introduced by Bonato, Janssen, and Roshanbin [Lecture Notes in Computer Science 8882 (2014)] to measure the speed of the spread of contagion in a graph. They proved for any connected graph G of order n, b(G) ≤ 2 √n − 1, and conjectured that b(G) ≤ √n . In this paper, we proved b(G) ≤ −3+ √ 24n+33 4 , which is roughly √ 6 2 √ n. We also settled the following conjecture of Bonato-Janssen-Roshanbin: b(G)b(Ḡ) ≤ n + 4 provided both G and Ḡ are connected.

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