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A note on hyperopic cops and robber

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arxiv 2107.07368 v1 pith:BZT2S7QB submitted 2021-07-15 math.CO cs.DM

A note on hyperopic cops and robber

classification math.CO cs.DM
keywords copshyperopicnumberrobbercommongraphsneighbourhoodanalogous
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We explore a variant of the game of Cops and Robber introduced by Bonato et al.~where the robber is invisible unless outside the common neighbourhood of the cops. The hyperopic cop number is analogous to the cop number and we investigate bounds on this quantity. We define a small common neighbourhood set and relate the minimum cardinality of this graph parameter to the hyperopic cop number. We consider diameter 2 graphs, particularly the join of two graphs, as well as Cartesian products.

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