Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647053 | Discrete Mathematics | 2016 | 5 Pages |
Abstract
We consider a variation of cop vs. robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on V(G)V(G) and moves according to this fixed distribution. The cop moves from vertex to adjacent vertex with the goal of minimizing expected capture time. Players move simultaneously. We show that when the gambler’s distribution is known, the expected capture time (with best play) on any connected nn-vertex graph is exactly nn. We also give bounds on the (generally greater) expected capture time when the gambler’s distribution is unknown to the cop.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Natasha Komarov, Peter Winkler,