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The game of overprescribed Cops and Robbers played on graphs. (English) Zbl 1371.05179
Summary: We consider the effect on the length of the game of Cops and Robbers when more cops are added to the game play. In Overprescribed Cops and Robbers, as more cops are added, the capture time (the minimum length of the game assuming optimal play) monotonically decreases. We give the full range of capture times for any number of cops on trees, and classify the capture time for an asymptotic number of cops on grids, hypercubes, and binomial random graphs. The capture time of planar graphs with a number of cops at and far above the cop number is considered.

MSC:
05C57 Games on graphs (graph-theoretic aspects)
91A43 Games involving graphs
91A24 Positional games (pursuit and evasion, etc.)
05C10 Planar graphs; geometric and topological aspects of graph theory
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