# A tandem version of the cops and robber game played on products of graphs

Nancy E. Clarke; Richard J. Nowakowski

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 3, page 241-249
- ISSN: 2083-5892

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topNancy E. Clarke, and Richard J. Nowakowski. "A tandem version of the cops and robber game played on products of graphs." Discussiones Mathematicae Graph Theory 25.3 (2005): 241-249. <http://eudml.org/doc/270333>.

@article{NancyE2005,

abstract = {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.},

author = {Nancy E. Clarke, Richard J. Nowakowski},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {game; cop; tandem-win; pursuit; graph; product},

language = {eng},

number = {3},

pages = {241-249},

title = {A tandem version of the cops and robber game played on products of graphs},

url = {http://eudml.org/doc/270333},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Nancy E. Clarke

AU - Richard J. Nowakowski

TI - A tandem version of the cops and robber game played on products of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 3

SP - 241

EP - 249

AB - 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.

LA - eng

KW - game; cop; tandem-win; pursuit; graph; product

UR - http://eudml.org/doc/270333

ER -

## References

top- [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). Zbl0919.05001
- [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. Zbl1073.05060
- [4] W. Imrich and H. Izbicki, Associative Products of Graphs, Monatshefte für Mathematik 80 (1975) 277-281, doi: 10.1007/BF01472575. Zbl0328.05136
- [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. Zbl0615.05049
- [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. Zbl0957.91029
- [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. Zbl0508.05058
- [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. Zbl0636.90050

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