Bonato, Janssen, and Roshanbin's burning number conjecture

Let GG be a connected graph of order nn, and let b(G)b(G) denote its burning number. Bonato, Janssen, and Roshanbin's conjecture.

b(G)n.b(G)\leq \left\lceil\sqrt{n}\right\rceil.

This conjecture would improve the general bound b(G)2n1b(G)\leq 2\left\lceil\sqrt{n}\right\rceil-1 and seeks the sharp order-of-magnitude upper bound for the burning number of connected graphs. It is presented as an open problem.

Sources & referencesView supporting material

Primary source

Stéphane Bessy, Anthony Bonato, Jeannette Janssen and Dieter Rautenbach, “Bounds on the Burning Number”, arXiv:1511.06023 (2016).

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