Abstract
AbstractThe game of Cops and Robbers is a well‐known pursuit‐evasion game played on graphs. It has been proved that cubic graphs can have arbitrarily large cop number , but the known constructions show only that the set is unbounded. In this paper, we prove that there are arbitrarily large subcubic graphs whose cop number is at least where . We also show that proving Meyniel's conjecture for graphs of bounded degree implies a weaker version of Meyniel's conjecture for all graphs.
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