1 citations · 8 across the 24 of their papers we have counts for
7 papers · 1 filter
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…
The isoperimetric peak of complete trees
Anthony Bonato, Lazar Mandic, Trent G. Marbach +1
We give exact values and bounds on the isoperimetric peak of complete trees, improving on known results. For the complete -ary tree of depth , if , then we find that…
Locally finite graphs and their localization numbers
Anthony Bonato, Florian Lehner, Trent G. Marbach +1
We study the Localization game on locally finite graphs trees, where each of the countably many vertices have finite degree. In contrast to the finite case, we construct a locally…
Tic-Tac-Toe on Designs
Peter Danziger, Melissa A. Huggan, Rehan Malik +1
We consider playing the game of Tic-Tac-Toe on block designs BIBD() and transversal designs TD(). Players take turns choosing points and the first player to complete…
How to cool a graph
Anthony Bonato, Trent G. Marbach, Holden Milne +1
We introduce a new graph parameter called the cooling number, inspired by the spread of influence in networks and its predecessor, the burning number. The cooling number measures t…