Bounding the cop number of a graph by its genus

Joshua Erde, Florian Lehner, Max Pitz, Nathan Bowler

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

Abstract

The game of cops and robbers is a pursuit game played on a graph G in which a group of cops tries to catch a robber, where both are allowed to move along to edges of G. The cop number of G, denoted by c(G), is the smallest number of cops needed to catch a robber on G. Schröder showed that c(G) is at most 3/2 g(G) + 3, where g(G) is the genus of G, that is, the smallest k such that G can be drawn on an orientable surface of genus k. Furthermore, he conjectured that this bound could be improved to g(G) +3. By relating the game of cops and robbers to a topological game played on a surface we prove that c(G) is at most 4/3 g(G) +3.
Originalspracheenglisch
TitelProceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019)
Seiten507-510
PublikationsstatusVeröffentlicht - 2019

Publikationsreihe

NameActa Mathematica Universitatis Comenianae

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Genus
Game
Topological Games
Graph in graph theory
Pursuit

Dies zitieren

Erde, J., Lehner, F., Pitz, M., & Bowler, N. (2019). Bounding the cop number of a graph by its genus. in Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019) (S. 507-510). (Acta Mathematica Universitatis Comenianae).

Bounding the cop number of a graph by its genus. / Erde, Joshua; Lehner, Florian; Pitz, Max; Bowler, Nathan .

Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019). 2019. S. 507-510 (Acta Mathematica Universitatis Comenianae).

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

Erde, J, Lehner, F, Pitz, M & Bowler, N 2019, Bounding the cop number of a graph by its genus. in Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019). Acta Mathematica Universitatis Comenianae, S. 507-510.
Erde J, Lehner F, Pitz M, Bowler N. Bounding the cop number of a graph by its genus. in Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019). 2019. S. 507-510. (Acta Mathematica Universitatis Comenianae).
Erde, Joshua ; Lehner, Florian ; Pitz, Max ; Bowler, Nathan . / Bounding the cop number of a graph by its genus. Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019). 2019. S. 507-510 (Acta Mathematica Universitatis Comenianae).
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