منابع مشابه
The Robber Locating game
In 2012 Seager introduced a new variant of the Cops and Robbers game, in which a cop searches for a moving robber on a graph using distance probes. The robber on his turn can either remain still or move to an adjacent vertex, while the cop on her turn probes any vertex and learns the robber’s distance from the probed vertex. Carraher, Choi, Delcourt, Erickson and West later showed that for any ...
متن کاملCops and Robber Game with a Fast Robber on Interval, Chordal, and Planar Graphs
We consider a variant of the Cops and Robber game, introduced by Fomin, Golovach, Kratochv́ıl, 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 through a vertex occupied by a cop. We study this game on interval graphs, chordal graphs, planar graphs, and hypercube graphs. Let c∞(G) denote the number of cops needed to captu...
متن کاملVariations of the cop and robber game on graphs
We prove new theoretical results about several variations of the cop and robber game on graphs. First, we consider a variation of the cop and robber game which is more symmetric called the cop and killer game. We prove for all c < 1 that almost all random graphs are stalemate for the cop and killer game, where each edge occurs with probability p such that 1 nc ≤ p ≤ 1 − 1 nc . We prove that a g...
متن کاملCop and robber game and hyperbolicity
In this note, we prove that all cop-win graphs G in the game in which the robber and the cop move at different speeds s and s′ with s′ < s, are δ-hyperbolic with δ = O(s). We also show that the dependency between δ and s is linear if s − s′ = Ω(s) and G obeys a slightly stronger condition. This solves an open question from the paper J. Chalopin et al., Cop and robber games when the robber can h...
متن کاملA witness version of the Cops and Robber game
The games considered aremixtures of Searching andCops andRobber. The cops havepartial information provided viawitnesseswho report ‘‘sightings’’ of the robber. Thewitnesses are able to provide information about the robber’s position but not the direction in which he is moving. The robber has perfect information. In the case when sightings occur at regular intervals, we present a recognition theo...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1987
ISSN: 0166-218X
DOI: 10.1016/0166-218x(87)90034-5