Author

William B. Kinnersley

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Preprint Sep 2026

On the Burning Game: Nordhaus-Gaddum Bounds and Graph Products

We continue research on the burning game on graphs. Given a graph $G$, two players, Burner and Staller, take turns in selecting vertices of $G$ to burn. All burned vertices spread fire to unburned neighboring vertices, as in the burning process. The goal of Burner is to burn the graph as quickly as possible, while Stal...

Nina Chiarelli, Vesna Irvsivc Chenoweth, Marko Jakovac et al. · 0 citations

Preprint Aug 2026

On the damage number of graphs

We study a variant of Cops and Robbers in which the robber attempts to visit as many vertices of the graph as possible without being captured, while the cop aims to keep the robber confined to a small set of vertices. The \textit{damage number} of a graph $G$, introduced by Cox and Sanaei in 2019, is the maximum number...

Valentin Gledel, William B. Kinnersley, Balázs Patkós et al. · 0 citations