4 papers · 2 filters
A note on non-isomorphic edge-color classes in random graphs
Patrick Bennett, Ryan Cushman, Andrzej Dudek +1
For a graph , let be the maximum number of colors such that there exists an edge-coloring of with no two color classes being isomorphic. We investigate the behavior o…
The Localization Game on Directed Graphs
Anthony Bonato, Ryan Cushman, Trent G. Marbach +1
In the Localization game played on graphs, a set of cops uses distance probes to identify the location of an invisible robber. We present an extension of the game and its main para…
The Erdős-Gyárfás function -- so Gyárfás was right
Patrick Bennett, Ryan Cushman, Andrzej Dudek +1
A -coloring of is an edge-coloring of where every -clique spans at least five colors. We show that there exist -colorings of using $\frac 56 n…
On Meyniel extremal families of graphs
Anthony Bonato, Ryan Cushman, Trent G. Marbach
We provide new constructions of Meyniel extremal graphs, which are families of graphs with the conjectured largest asymptotic cop number. Using spanning subgraphs, we prove that th…