8 papers
On the Burning Game: Nordhaus-Gaddum Bounds and Graph Products
Nina Chiarelli, Vesna Iršič Chenoweth, Marko Jakovac +2
We continue research on the burning game on graphs. Given a graph , two players, Burner and Staller, take turns in selecting vertices of to burn. All burned vertices spread…
The directional localization game on graphs
John Jones, William B. Kinnersley
In the localization game on a graph , a team of cops searches for an invisible, mobile robber on by "probing" vertices; each probe tells the cops the distance from the probe…
On the damage number of graphs
Valentin Gledel, William B. Kinnersley, Balázs Patkós +1
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…
Limited-visibility Cops and Robbers on Hamming graphs
John Jones, William B. Kinnersley
In the classic game of Cops and Robbers, a team of cops pursues a robber through a graph. The traditional model of Cops and Robbers operates under the assumption that the cops know…
The burning game on graphs
Nina Chiarelli, Vesna Iršič, Marko Jakovac +2
Motivated by the burning and cooling processes, the burning game is introduced. Two players (Burner and Staller) play the game on a graph by alternately selecting vertices of $…
The Game Saturation Number of a Graph
James M. Carraher, William B. Kinnersley, Benjamin Reiniger +1
Given a family and a host graph , a graph is -saturated relative to if no subgraph of lies in but adding any e…
Lazy Cops and Robbers played on Graphs
Deepak Bal, Anthony Bonato, William B. Kinnersley +1
We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. We investigate the analogue of the cop number for…
Chain-making games in grid-like posets
Daniel W. Cranston, William B. Kinnersley, Kevin G. Milans +2
We study the Maker-Breaker game on the hypergraph of chains of fixed size in a poset. In a product of chains, the maximum size of a chain that Maker can guarantee building is $k-\l…