A note on hyperopic cops and robber

Abstract

In this paper, 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 neighborhood 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 neighborhood set and relate the minimum cardinality of this graph parameter to the hyperopic cop number. We consider diameter [Formula: see text] graphs, particularly the join of two graphs, as well as Cartesian products.