On the cop number of toroidal graphs

Journal of Combinatorial Theory, Series B - Tập 151 - Trang 250-262 - 2021
Florian Lehner

Tài liệu tham khảo

Aigner, 1984, A game of cops and robbers, Discrete Appl. Math., 8, 1, 10.1016/0166-218X(84)90073-8 Andreae, 1986, On a pursuit game played on graphs for which a minor is excluded, J. Comb. Theory, Ser. B, 41, 37, 10.1016/0095-8956(86)90026-2 Baird, 2012, Meyniel's conjecture on the cop number: a survey, J. Comb., 3, 225 Bonato, 2020, Topological directions in cops and robbers, J. Comb., 11, 47 Bonato, 2011, vol. 61 N. Bowler, J. Erde, F. Lehner, M. Pitz, Bounding the cop number of a graph by its genus, preprint, 2019. Clarke, 2014, A note on the cops and robber game on graphs embedded in non-orientable surfaces, Graphs Comb., 30, 119, 10.1007/s00373-012-1246-z B. Mohar, Notes on cops and robber game on graphs, 2008, Unpublished note. Nowakowski, 1983, Vertex-to-vertex pursuit in a graph, Discrete Math., 43, 235, 10.1016/0012-365X(83)90160-7 Quilliot, 1978 Quilliot, 1985, A short note about pursuit games played on a graph with a given genus, J. Comb. Theory, Ser. B, 38, 89, 10.1016/0095-8956(85)90093-0 Schroeder, 2001, The copnumber of a graph is bounded by ⌊32 genus(G)⌋+3, 243