@inproceedings{9a432bf2afcf4092b665410b47a96b32,

title = "Improved Bounds on the Cop Number of a Graph Drawn on a Surface",

abstract = "It is known that the cop number c(G) of a connected graph G can be bounded as a function of the genus of the graph g(G). It is conjectured by Schr{\"o}der that c(G) ≤ g(G) + 3. Recently, by relating this problem to a topological game, the authors, together with Bowler and Pitz, gave the current best known bound that c(G)≤4g(G)3+103. Combining some of these ideas with some techniques introduced by Schr{\"o}der we improve this bound and show that c(g)≤(1+o(1))(3-3)g≈1.268g.",

keywords = "Cops and Robbers, Genus, Graph searching",

author = "Joshua Erde and Florian Lehner",

year = "2021",

doi = "10.1007/978-3-030-83823-2_18",

language = "English",

volume = "14",

series = "Trends in Mathematics",

publisher = "Springer",

pages = "111--116",

booktitle = "Trends in Mathematics",

note = "European Conference on Combinatorics, Graph Theory and Applications : EuroComb 2021 ; Conference date: 06-09-2021 Through 10-09-2021",

}