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

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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.
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game   cop   tandem-win   pursuit   graph   product  
  • Acadia University, Wolfville, Nova Scotia
  • Dalhousie University, Halifax, Nova Scotia
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  • [3] N.E. Clarke and R.J. Nowakowski, Tandem-win Graphs, to appear in Discrete Math.
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  • [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.
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