Cops and Robbers Playing on Edges
نویسنده
چکیده
In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. In this paper, we consider the variant of the game in which both players play on edges instead of vertices, yielding the edge cop number. We relate the new graph parameter to the classic one, investigate Meyniel extremal families, and characterize edge cop-win graphs. We also play the game on random graphs and planar graphs.
منابع مشابه
The Cop Number of the One-Cop-Moves Game on Planar Graphs
Cops and robbers is a vertex-pursuit game played on graphs. In the classical cops-and-robbers game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph’s edges with perfect information about each other’s positions. If a cop eventually occupies the same vertex as the robber, then the cops win; the robber wins if she can indefinitely evade capture. Aig...
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