2 citations · 2 across the 5 of their papers we have counts for
6 papers · 1 filter
The Pyro game: a slow intelligent fire
Margaret-Ellen Messinger, Spencer Yarnell
In the Firefighter problem, a fire breaks out at a vertex of a graph and at each subsequent time step, the firefighter chooses a vertex to protect and then the fire spreads from ea…
A note on hyperopic cops and robber
Nancy E. Clarke, Stephen Finbow, Margaret-Ellen Messinger +1
We explore a variant of the game of Cops and Robber introduced by Bonato et al.~where the robber is invisible unless outside the common neighbourhood of the cops. The hyperopic cop…
A Note on the Parallel Cleaning of Cliques
Alejandro Angeli Ayello, Margaret-Ellen Messinger
We disprove a conjecture proposed in [Gaspers et al., Discrete Applied Mathematics, 2010] and provide a new upper bound for the minimum number of brushes required to continually pa…
Hyperopic Cops and Robbers
A. Bonato, N. E. Clarke, D. Cox +3
We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the…
Disjoint Dominating Sets with a Perfect Matching
William F. Klostermeyer, Margaret-Ellen Messinger, Alejandro Angeli Ayello
In this paper, we consider dominating sets and such that and are disjoint and there exists a perfect matching between them. Let denote the ca…
Bounding the search number of graph products
N. E. Clarke, M. E. Messinger, G. Power
In this paper, we provide results for the search number of the Cartesian product of graphs. We consider graphs on opposing ends of the spectrum: paths and cliques. Our main result…