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CORR
2016
Springer

Visibility Graphs, Dismantlability, and the Cops and Robbers Game

7 years 12 months ago
Visibility Graphs, Dismantlability, and the Cops and Robbers Game
We study versions of cop and robber pursuit-evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player’s location, players take turns, and the robber is captured when the cop arrives at the same point as the robber. In visibility graphs we show the cop can always win because visibility graphs are dismantlable, which is interesting as one of the few results relating visibility graphs to other known graph classes. We extend this to show that the cop wins games in which players move along straight line segments inside any polygon and, more generally, inside any simply connected planar region with a reasonable boundary. Essentially, our problem is a type of pursuit-evasion using the link metric rather than the Euclidean metric, and our result provides an interesting class of infinite cop-win graphs.
Anna Lubiw, Jack Snoeyink, Hamideh Vosoughpour
Added 01 Apr 2016
Updated 01 Apr 2016
Type Journal
Year 2016
Where CORR
Authors Anna Lubiw, Jack Snoeyink, Hamideh Vosoughpour
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