%A Gonzalez Hermosillo de la Maza, Sebastian
%A Mohar, Bojan
%D 2019
%T Guarding isometric subgraphs and Lazy Cops and Robbers
%K
%X In the game of Cops and Robbers, one of the most useful results is that an isometric path in a graph can be guarded by one cop. In this paper, we introduce the concept of wide shadow on a graph, and use it to provide a short proof of the characterization of $1$-guardable graphs. As an application, we show that $3$ cops can capture a robber in any planar graph with the added restriction that at most two cops can move simultaneously, proving a conjecture of Yang and strenghtening a classical result by Aigner and Fromme.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1304
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 743-747%V 88
%N 3
%@ 0862-9544
%8 2019-07-30