English

A note on hyperopic cops and robber

Combinatorics 2021-07-16 v1 Discrete Mathematics

Abstract

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.

Keywords

Cite

@article{arxiv.2107.07368,
  title  = {A note on hyperopic cops and robber},
  author = {Nancy E. Clarke and Stephen Finbow and Margaret-Ellen Messinger and Amanda Porter},
  journal= {arXiv preprint arXiv:2107.07368},
  year   = {2021}
}
R2 v1 2026-06-24T04:13:55.498Z