196 citations · 319 across the 19 of their papers we have counts for
4 papers · 1 filter
On the density of nearly regular graphs with a good edge-labelling
Abbas Mehrabian
A good edge-labelling of a simple graph is a labelling of its edges with real numbers such that, for any ordered pair of vertices (u,v), there is at most one nondecreasing path fro…
Cops and Robber Game with a Fast Robber on Expander Graphs and Random Graphs
Abbas Mehrabian
We consider a variant of the Cops and Robber game, in which the robber has unbounded speed, i.e. can take any path from her vertex in her turn, but she is not allowed to pass throu…
The capture time of grids
Abbas Mehrabian
We consider the game of Cops and Robber played on the Cartesian product of two trees. Assuming the players play perfectly, it is shown that if there are two cops in the game, then…
Lower Bounds for the Cop Number When the Robber is Fast
Abbas Mehrabian
We consider a variant of the Cops and Robbers game where the robber can move t edges at a time, and show that in this variant, the cop number of a d-regular graph with girth larger…