Some results about pursuit games on metric spaces obtained through graph theory techniques
European Journal of Combinatorics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Complexity of the cop and robber guarding game
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
How to guard a graph against tree movements
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
How to guard a graph against tree moves
Information Processing Letters
The guarding game is E-complete
Theoretical Computer Science
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A cop-robber guarding game is played by the robber-player and the cop-player on a graph G with a partition R and C of the vertex set. The robber-player starts the game by placing a robber (her pawn) on a vertex in R, followed by the cop-player who places a set of cops (her pawns) on some vertices in C. The two players take turns in moving their pawns to adjacent vertices in G. The cop-player moves the cops within C to prevent the robber-player from moving the robber to any vertex in C. The robber-player wins if it gets a turn to move the robber onto a vertex in C on which no cop situates, and the cop-player wins otherwise. The problem is to find the minimum number of cops that admits a winning strategy to the cop-player. It has been shown that the problem is polynomially solvable if R induces a path, whereas it is NP-complete if R induces a tree. In this paper, we show that the problem remains NP-complete even if R induces a 3-star and that the problem is polynomially solvable if R induces a cycle.