منابع مشابه
Hyperopic 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, 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...
متن کاملLimited Visibility Cops and Robbers
We consider a variation of the Cops and Robber game where the cops can only see the robber when the distance between them is at most a fixed parameter `. We consider the basic consequences of this definition for some simple graph families, and show that this model is not monotonic, unlike common models where the robber is invisible. We see that cops’ strategy consists of a phase in which they n...
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 کاملSimultaneously moving cops and robbers
In this paper we study the concurrent cops and robber (CCCR) game. CCCR follows the same rules as the classical, turn-based game, except for the fact that the players move simultaneously. The cops' goal is to capture the robber and the concurrent cop number of a graph is defined the minimum number of cops which guarantees capture. For the variant in which it it required to capture the robber in...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2019
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2018.10.004