A tandem version of the cops and robber game played on products of graphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 241-249.

Voir la notice de l'article provenant de la source Library of Science

In this version of the Cops and Robber game, the cops move in tandems, or pairs, such that they are at distance at most one from each other after every move. The problem is to determine, for a given graph G, the minimum number of tandems sufficient to guarantee a win for the cops. We investigate this game on three graph products, the Cartesian, categorical and strong products.
Keywords: game, cop, tandem-win, pursuit, graph, product
@article{DMGT_2005_25_3_a2,
     author = {Clarke, Nancy and Nowakowski, Richard},
     title = {A tandem version of the cops and robber game played on products of graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {241--249},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a2/}
}
TY  - JOUR
AU  - Clarke, Nancy
AU  - Nowakowski, Richard
TI  - A tandem version of the cops and robber game played on products of graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2005
SP  - 241
EP  - 249
VL  - 25
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a2/
LA  - en
ID  - DMGT_2005_25_3_a2
ER  - 
%0 Journal Article
%A Clarke, Nancy
%A Nowakowski, Richard
%T A tandem version of the cops and robber game played on products of graphs
%J Discussiones Mathematicae. Graph Theory
%D 2005
%P 241-249
%V 25
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a2/
%G en
%F DMGT_2005_25_3_a2
Clarke, Nancy; Nowakowski, Richard. A tandem version of the cops and robber game played on products of graphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 241-249. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a2/

[1] A. Brandstädt, V.B. Le and J.P. Spinrad, Graph classes: a survey, SIAM Monographs on Discrete Math. and Appl., Society for Industrial and Applied Mathematics (SIAM) (Philadelphia, PA, 1999).

[2] N.E. Clarke, Constrained Cops and Robber (Ph.D. Thesis, Dalhousie University, 2002).

[3] N.E. Clarke and R.J. Nowakowski, Tandem-win Graphs, to appear in Discrete Math.

[4] W. Imrich and H. Izbicki, Associative Products of Graphs, Monatshefte für Mathematik 80 (1975) 277-281, doi: 10.1007/BF01472575.

[5] M. Maamoun and H. Meyniel, On a game of policeman and robber, Discrete Appl. Math. 17 (1987) 307-309, doi: 10.1016/0166-218X(87)90034-5.

[6] S. Neufeld and R.J. Nowakowski, A Game of Cops and Robbers Played on Products of Graphs, Discrete Math. 186 (1998) 253-268, doi: 10.1016/S0012-365X(97)00165-9.

[7] R.J. Nowakowski and P. Winkler, Vertex to vertex pursuit in a graph, Discrete Math. 43 (1983) 23-29, doi: 10.1016/0012-365X(83)90160-7.

[8] A. Quilliot, Thèse d'Etat (Université de Paris VI, 1983).

[9] R. Tosić, The search number of the Cartesian product of graphs, Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak., Ser. Mat. 17 (1987) 239-243.