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LAZY COPS AND ROBBERS ON HYPERCUBES
"... Abstract. 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 Ojak ..."
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and Ojakian, who provided asymptotic upper and lower bounds on the lazy cop number of the hypercube. By coupling the probabilistic method with a potential function argument, we improve on the existing lower bounds for the lazy cop number of hypercubes. 1.
Lower bounds for the cop number when the robber is fast
 Combinatorics, Probability and Computing
"... ar ..."
Cops and Robbers on Geometric Graphs
, 2011
"... Cops and robbers is a turnbased pursuit game played on a graph G. One robber is pursued by a set of cops. In each round, these agents move between vertices along the edges of the graph. The cop number c(G) denotes the minimum number of cops required to catch the robber in finite time. We study the ..."
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Cops and robbers is a turnbased pursuit game played on a graph G. One robber is pursued by a set of cops. In each round, these agents move between vertices along the edges of the graph. The cop number c(G) denotes the minimum number of cops required to catch the robber in finite time. We study
Cops and robber game with a fast robber
, 2011
"... Graph searching problems are described as games played on graphs, between a set of searchers and a fugitive. Variants of the game restrict the abilities of the searchers and the fugitive and the corresponding search number (the least number of searchers that have a winning strategy) is related to ..."
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over the cops. This version was first studied in 2008. We show that when the robber has speed s, the cop number of a connected nvertex graph can be as large as Ω(ns/s+1). This improves the Ω(n s−3 s−2) lower bound of Frieze, Krivelevich, and Loh (Variations on Cops and Robbers, J. Graph Theory
LAZY 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 p ..."
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provided asymptotic upper and lower bounds on the lazy cop number of the hypercube. By investigating expansion properties, we provide asymptotically almost sure bounds on the lazy cop number of binomial random graphs G(n, p) for a wide range of p = p(n). By coupling the probabilistic method with a
Cops and robbers from a distance
 Theor. Comput. Sci
"... Abstract. Cops and Robbers is a pursuit and evasion game played on graphs that has received much attention. We consider an extension of Cops and Robbers, distance k Cops and Robbers, where the cops win if at least one of them is of distance at most k from the robber in G. The cop number of a graph G ..."
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Cited by 2 (0 self)
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Abstract. Cops and Robbers is a pursuit and evasion game played on graphs that has received much attention. We consider an extension of Cops and Robbers, distance k Cops and Robbers, where the cops win if at least one of them is of distance at most k from the robber in G. The cop number of a graph
COPS AND INVISIBLE ROBBERS: THE COST OF DRUNKENNESS
"... Abstract. We examine a version of the Cops and Robber (CR) game in which the robber is invisible, i.e., the cops do not know his location until they capture him. Apparently this game (CiR) has received little attention in the CR literature. We examine two variants: in the first the robber is adversa ..."
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Cited by 2 (0 self)
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regular trees, give some bounds for grids, and provide general upper and lower bounds for general classes of graphs. We also give an infinite family of graphs showing that iCOD can be arbitrarily close to any value in [2,∞). Finally, we briefly examine one more CiR variant, in which the robber is invisible
To Catch a Falling Robber
"... We consider a CopsandRobber game played on the subsets of an nset. The robber starts at the full set; the cops start at the empty set. In each round, each cop moves up one level by gaining an element, and the robber moves down one level by discarding an element. The question is how many cops are ..."
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are needed to ensure catching the robber when the robber reaches the middle level. Alan Hill posed the problem and provided a lower bound of 2n/2 for even n and
On a Generalization of Meyniel’s Conjecture on the Cops and Robbers Game
"... We consider a variant of the Cops and Robbers game where the robber can move s edges at a time, and show that in this variant, the cop number of a connected graph on n vertices can be as large as Ω(n s s+1). This improves the Ω(n s−3 s−2) lower bound of Frieze et al. [5], and extends the result of t ..."
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Cited by 9 (4 self)
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We consider a variant of the Cops and Robbers game where the robber can move s edges at a time, and show that in this variant, the cop number of a connected graph on n vertices can be as large as Ω(n s s+1). This improves the Ω(n s−3 s−2) lower bound of Frieze et al. [5], and extends the result
LAZY 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 up ..."
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upper and lower bounds on the analogue of the cop number of the hypercube. By investigating expansion properties, we provide asymptotically almost sure bounds on the lazy cop number of binomial random graphs G(n, p) for a wide range of p = p(n). We provide an upper bound for the lazy cop number
Results 1  10
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