Abstract
Cops and robber game on a directed graph \(\overrightarrow{D}\) initiates by Player 1 placing k cops and then Player 2 placing one robber on the vertices of \(\overrightarrow{D}\). After that, starting with Player 1, alternately the players may move each of their tokens to the adjacent vertices. Player 1 wins if, after a finite number of moves, a cop and the robber end up on the same vertex and Player 2 wins otherwise. However, depending on the type of moves the players make, there are three different models, namely, the normal cop model: both cops and robber move along the direction of the arcs; the strong cop model: cops can move along or against the direction of the arcs while the robber moves along them; and the weak cop model: the robber can move along or against the direction of the arcs while the cops move along them. A graph is cop-win if Player 1 playing with a single cop has a winning strategy. In this article, we study the three models on some families of oriented graphs and characterize the cop-win directed graphs for the third model.
This work is partially supported by the IFCAM project Applications of graph homomorphisms (MA/IFCAM/18/39).
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Notes
- 1.
GRASTA 2014: http://www-sop.inria.fr/coati/events/grasta2014/.
- 2.
An oriented graph is a directed graph without 2-cycles i.e. each edge has a direction. For the purposes of this article, they are the same.
- 3.
We use the term directed cycle instead of oriented cycle as it is commonly used.
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Das, S., Gahlawat, H., Sahoo, U.K., Sen, S. (2019). Cops and Robber on Some Families of Oriented Graphs. In: Colbourn, C., Grossi, R., Pisanti, N. (eds) Combinatorial Algorithms. IWOCA 2019. Lecture Notes in Computer Science(), vol 11638. Springer, Cham. https://doi.org/10.1007/978-3-030-25005-8_16
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