1 citations · 8 across the 24 of their papers we have counts for
5 papers · 1 filter
Tight Bounds on the Probabilistic Zero Forcing on Hypercubes and Grids
Natalie C. Behague, Trent Marbach, Pawel Pralat
Zero forcing is a deterministic iterative graph colouring process in which vertices are coloured either blue or white, and in every round, any blue vertices that have a single whit…
Tic-Tac-Toe on an Affine Plane of order 4
Peter Danziger, Melissa A. Huggan, Rehan Malik +1
The game of tic-tac-toe is well known. In particular, in its classic version it is famous for being unwinnable by either player. While classically it is played on a grid, it is nat…
The localization number and metric dimension of graphs of diameter 2
Anthony Bonato, Melissa A. Huggan, Trent Marbach
We consider the localization number and metric dimension of certain graphs of diameter , focusing on families of Kneser graphs and graphs without 4-cycles. For the Kneser graphs…
The localization number of designs
Anthony Bonato, Melissa A. Huggan, Trent Marbach
We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via d…
The Game of Cops and Eternal Robbers
Anthony Bonato, Melissa Huggan, Trent Marbach +1
We introduce the game of Cops and Eternal Robbers played on graphs, where there are infinitely many robbers that appear sequentially over distinct plays of the game. A positive int…