10 papers · 1 filter
Burning Steiner triple systems
Andrea C. Burgess, Peter H. Danziger, Caleb W. Jones +2
Graph burning is a round-based process which can be viewed as a discrete one-player game that models the spread of influence throughout a network. Extending this process to hypergr…
Cooling graph products
Anthony Bonato, MacKenzie Carr, Caleb Jones +2
The cooling number measures the speed at which a slow-moving influence or contagion spreads on a graph. In this paper, we investigate the cooling number of four classical graph pro…
Between burning and cooling: liminal burning on graphs
Anthony Bonato, Trent G. Marbach, John Marcoux +1
Liminal burning generalizes both the burning and cooling processes in graphs. In -liminal burning, a Saboteur reveals -sets of vertices in each round, with the goal of extend…
Hypergraph burning, matchings, and zero forcing
Anthony Bonato, Caleb Jones, Trent G. Marbach +2
Lazy burning is a recently introduced variation of burning where only one set of vertices is chosen to burn in the first round. In hypergraphs, lazy burning spreads when all but on…
Cuts, Cats, and Complete Graphs
Rylo Ashmore, Danny Dyer, Trent Marbach +1
We introduce the game of Cat Herding, where an omnipresent herder slowly cuts down a graph until an evasive cat player has nowhere to go. The number of cuts made is the score of a…
How to burn a Latin square
Anthony Bonato, Caleb Jones, Trent G. Marbach +1
We investigate the lazy burning process for Latin squares by studying their associated hypergraphs. In lazy burning, a set of vertices in a hypergraph is initially burned, and that…