Title: Hyperopic Cops and Robbers,
Abstract: We introduce a new variant of the game of Cops and Robbers played on graphs,
where the robber is invisible unless outside the neighbor set of a cop. The
hyperopic cop number is the corresponding analogue of the cop number, and we
investigate bounds and other properties of this parameter. We characterize the
cop-win graphs for this variant, along with graphs with the largest possible
hyperopic cop number. We analyze the cases of graphs with diameter 2 or at
least 3, focusing on when the hyperopic cop number is at most one greater than
the cop number. We show that for planar graphs, as with the usual cop number,
the hyperopic cop number is at most 3. The hyperopic cop number is considered
for countable graphs, and it is shown that for connected chains of graphs, the
hyperopic cop density can be any real number in $[0,1/2].$