Geodesic
Guarding isometric subgraphs and Lazy Cops and Robbers
Sebastian Gonzalez Hermosillo de la Maza1 ; Bojan Mohar1 ; Sebastian Gonzalez Hermosillo de la Maza ; Bojan Mohar
1Simon Fraser University, Department of Mathematics, Burnaby, Canada
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 743-747 
Sebastian Gonzalez Hermosillo de la Maza; Bojan Mohar; Sebastian Gonzalez Hermosillo de la Maza; Bojan Mohar. Guarding isometric subgraphs and Lazy Cops and Robbers. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 743-747. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a59/
@article{AMUC_2019_88_3_a59,
     author = {Sebastian Gonzalez Hermosillo de la Maza and Bojan Mohar and Sebastian Gonzalez Hermosillo de la Maza and Bojan Mohar},
     title = { Guarding isometric subgraphs and {Lazy} {Cops} and {Robbers}},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {743--747},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a59/}
}
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Voir la notice de l'article provenant de la source Comenius University

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.