Cops and Robbers on Graphs Based on Designs
نویسنده
چکیده
We investigate the cop number of graphs based on combinatorial designs. Incidence graphs, point graphs, and block intersection graphs are studied, with an emphasis on finding families of graphs with large cop number. We generalize known results on so-called Meyniel extremal families by supplying bounds on the incidence graph of transversal designs, certain G-designs, and BIBDs with λ ≥ 1. Families of graphs with diameter two, C4-free, and with unbounded chromatic number are described with the conjectured asymptotically maximum cop number.
منابع مشابه
The game of Overprescribed Cops and Robbers played on graphs
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 ...
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