Abstract
A cop-robber guarding game is played by the robber-player and the cop-player on a graph G with a bipartition {R,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 admit 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. It was open whether it is solvable or not when R induces a cycle. This paper answers the question affirmatively.
This is an extended abstract. This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Culture, Sports, Science and Technology of Japan.
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Nagamochi, H. (2009). Cop-Robber Guarding Game with Cycle Robber Region . In: Deng, X., Hopcroft, J.E., Xue, J. (eds) Frontiers in Algorithmics. FAW 2009. Lecture Notes in Computer Science, vol 5598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02270-8_10
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DOI: https://doi.org/10.1007/978-3-642-02270-8_10
Publisher Name: Springer, Berlin, Heidelberg
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