منابع مشابه
Variations on cops and robbers
We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R > 1 edges at a time, establishing a general upper bound of n/α √ log α , where α = 1 + 1 R , thus generalizing the best known upper bound for the classical case R = 1 due to Lu and Peng. We also show that in this case, the cop number of an n-vertex graph can be as large as n 1 R...
متن کاملHyperopic Cops and Robbers
We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic c...
متن کاملCops and Robbers on Intersection Graphs
The game of cops and robber, introduced by Nowakowski and Winkler in 1983, is played by two players on a graph G, one controlling k cops and the other one robber, all positioned on VG. The players alternate in moving their pieces to distance at most 1 each. The cops win if they capture the robber, the robber wins by escaping indefinitely. The copnumber of G, that is the smallest k such that k c...
متن کاملLazy Cops and Robbers on Hypercubes
We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. We investigate the analogue of the cop number for this game, which we call the lazy cop number. Lazy Cops and Robbers was recently introduced by Offner and Ojakian, who provided asymptotic upper and lower bounds on the lazy cop number of the hypercube. By coupling th...
متن کاملCops, robbers, and infinite graphs
We study the simplest variant of the cops and robbers game, where one cop tries to catch one robber by moving along the edges of a graph. A well known result connected to this game is that on a finite graph the cop has a winning strategy if and only if the graph is constructible. Chastand et al. proposed the notion of weakly cop-win graphs which they thought could lead to a generalisation of th...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2011
ISSN: 0364-9024
DOI: 10.1002/jgt.20591