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Bounds for Cops and Robber Pursuit
, 2009
"... Abstract. We prove that the robber can evade (that is, stay at least unit distance from) at least ⌊n/5.889 ⌋ cops patroling an n × n continuous square region, that a robber can always evade a single cop patroling a square with side length 4 or larger, and that a single cop on patrol can always captu ..."
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Abstract. We prove that the robber can evade (that is, stay at least unit distance from) at least ⌊n/5.889 ⌋ cops patroling an n × n continuous square region, that a robber can always evade a single cop patroling a square with side length 4 or larger, and that a single cop on patrol can always
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.
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 (1−o(1))√logα n 1, where α = 1 + R, thus generalizing the best known upper bound for the classical case R = 1 due to ..."
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Cited by 10 (1 self)
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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 (1−o(1))√logα n 1, where α = 1 + R, thus generalizing the best known upper bound for the classical case R = 1 due
Lower bounds for the cop number when the robber is fast
 Combinatorics, Probability and Computing
"... ar ..."
The game of Wall Cops and Robbers⋆
"... Abstract. Wall Cops and Robbers is a new vertex pursuit game played on graphs, inspired by both the games of Cops and Robbers and Conway’s Angel Problem. In the game, the cops are free to move to any vertex and build a wall; once a vertex contains a wall, the robber may not move there. Otherwise, th ..."
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Abstract. Wall Cops and Robbers is a new vertex pursuit game played on graphs, inspired by both the games of Cops and Robbers and Conway’s Angel Problem. In the game, the cops are free to move to any vertex and build a wall; once a vertex contains a wall, the robber may not move there. Otherwise
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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Cited by 1 (0 self)
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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 WITH CONSTRAINTS
, 2012
"... Cops & Robber is a classical pursuitevasion game on undirected graphs, where the task is to identify the minimum number of cops sufficient to catch the robber. In this paper, we investigate the changes in problem’s complexity and combinatorial properties with constraining the following natural ..."
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Cited by 1 (0 self)
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Cops & Robber is a classical pursuitevasion game on undirected graphs, where the task is to identify the minimum number of cops sufficient to catch the robber. In this paper, we investigate the changes in problem’s complexity and combinatorial properties with constraining the following
CONJECTURES ON COPS AND ROBBERS
"... Abstract. We consider some of the most important conjectures in the study of the game of Cops and Robbers and the cop number of a graph. The conjectures touch on diverse areas such as algorithmic, topological, and structural graph theory. 1. ..."
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Abstract. We consider some of the most important conjectures in the study of the game of Cops and Robbers and the cop number of a graph. The conjectures touch on diverse areas such as algorithmic, topological, and structural graph theory. 1.
COPS AND ROBBERS PLAYING ON EDGES
"... Abstract. In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. In this paper, we consider the variant of the game in which both players play on edges instead ..."
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Cited by 1 (0 self)
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Abstract. In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. In this paper, we consider the variant of the game in which both players play on edges instead
Results 1  10
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