منابع مشابه
Lazy 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 کاملLazy Cops and Robbers Played on Graphs
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 investigati...
متن کاملVariations 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 کاملLazy Cops and Robbers Played on Random Graphs and Graphs on Surfaces
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. The lazy cop number is the analogue of the usual cop number for this game. Lazy Cops and Robbers was recently introduced by Offner and Ojakian, who provided asymptotic upper and lower bounds on the analogue of the cop number of the hypercube. By investigating expansi...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2015
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548314000807