Cops and Robber on Hyperbolic Manifolds
EUROCOMB’23
615–622
M. Aigner and M. Fromme. A game of cops and robbers. Discrete Appl. Math., 8(1):1-11, 1984.
https://doi.org/10.1016/0166-218X(84)90073-8
James W Anderson. Convexity, area, and trigonometry. In Hyperbolic Geometry, pages 111-151. Springer, 1999.
https://doi.org/10.1007/978-1-4471-3987-4_5
Riccardo Benedetti and Carlo Petronio. Lectures on hyperbolic geometry. Springer Science & Business Media, 1992.
https://doi.org/10.1007/978-3-642-58158-8
Andrew Beveridge and Yiqing Cai. Two-dimensional pursuit-evasion in a compact domain with piecewise analytic boundary. ArXiv e-prints, May 2015.
Béla Bollobás, Gábor Kun, and Imre Leader. Cops and robbers in a random graph. Journal of Combinatorial Theory, Series B, 103(2):226-236, 2013.
https://doi.org/10.1016/j.jctb.2012.10.002
Anthony Bonato. An invitation to pursuit-evasion games and graph theory, volume 97 of Student Mathematical Library. American Mathematical Society, Providence, RI, 2022.
https://doi.org/10.1090/stml/097
Anthony Bonato and Richard J. Nowakowski. The game of cops and robbers on graphs, volume 61 of Student Mathematical Library. American Mathematical Society, Providence, RI, 2011.
https://doi.org/10.1090/stml/061
Nathan Bowler, Joshua Erde, Florian Lehner, and Max Pitz. Bounding the cop number of a graph by its genus. SIAM J. Discrete Math., 35(4):2459-2489, 2021.
https://doi.org/10.1137/20M1312150
Peter Bradshaw. A proof of the meyniel conjecture for abelian cayley graphs. Discrete Mathematics, 343(1):111546, 2020.
https://doi.org/10.1016/j.disc.2019.06.002
H. T. Croft. 'Lion and man': A postscript. J. Lond. Math. Soc., 39:385-390, 1964.
https://doi.org/10.1112/jlms/s1-39.1.385
Joshua Erde and Florian Lehner. Improved bounds on the cop number of a graph drawn on a surface. In Extended Abstracts EuroComb 2021, pages 111-116. Springer, 2021.
https://doi.org/10.1007/978-3-030-83823-2_18
Peter Frankl. Cops and robbers in graphs with large girth and Cayley graphs. Discrete Appl. Math., 17(3):301-305, 1987.
https://doi.org/10.1016/0166-218X(87)90033-3
Heinz Hopf. Zum Clifford-Kleinschen Raumproblem. Math. Ann., 95(1):313-339, 1926.
https://doi.org/10.1007/BF01206614
Vesna Iršič, Bojan Mohar, and Alexandra Wesolek. Cops and robber on hyperbolic manifolds. In preparation.
Vesna Iršič, Bojan Mohar, and Alexandra Wesolek. Cops and robber game in higher-dimensional manifolds with spherical and Euclidean metric. C. R. Math. Acad. Sci. Soc. R. Can., 44(3):50-68, 2022.
Gwenaël Joret, Marcin Kamiński, and Dirk Oliver Theis. The cops and robber game on graphs with forbidden (induced) subgraphs. Contrib. Discrete Math., 5(2):40-51, 2010.
Wilhelm Killing. Ueber die Clifford-Klein'schen Raumformen. Math. Ann.,39(2):257-278, 1891.
https://doi.org/10.1007/BF01206655
J. E. Littlewood. Littlewood's miscellany. Cambridge University Press, Cambridge, 1986. Edited and with a foreword by Béla Bollobás.
Tomasz Łuczak and Paweł Prałat. Chasing robbers on random graphs: zigzag theorem. Random Structures & Algorithms, 37(4):516-524, 2010.
https://doi.org/10.1002/rsa.20338
Bojan Mohar. Notes on cops and robber game on graphs. ArXiv e-prints, October 2017.
Bojan Mohar. Min-max theorem for the game of cops and robber on geodesic spaces. ArXiv e-prints, December 2021.
Bojan Mohar. The game of cops and robber on geodesic spaces. ArXiv e-prints, May 2022.
N. Yu. Satimov and A. Sh. Kuchkarov. On the solution of a model differential pursuit-evasion game on a sphere. Uzb. Mat. Zh., 2000(1):45-50, 2000.
Bernd SW Schröder. The copnumber of a graph is bounded by [3/2 genus(g)]+ 3. In Categorical perspectives, pages 243-263. Springer, 2001.
https://doi.org/10.1007/978-1-4612-1370-3_14
Stothers, Wilson. Hyperbolic geometry. http://www.maths.gla.ac.uk/wws/cabripages/hyperbolic/hyperbolic0.html. [Online; accessed 16-January-2023].
Olga Yufereva. Lion and man game in compact spaces. Dyn. Games Appl.,9(1):281-292, 2019.
https://doi.org/10.1007/s13235-018-0239-9

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