### Abstract

Original language | English |
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Title of host publication | Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019) |

Pages | 507-510 |

Publication status | Published - 2019 |

### Publication series

Name | Acta Mathematica Universitatis Comenianae |
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### Fingerprint

### Cite this

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

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

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

}

TY - GEN

T1 - Bounding the cop number of a graph by its genus

AU - Erde, Joshua

AU - Lehner, Florian

AU - Pitz, Max

AU - Bowler, Nathan

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

M3 - Conference contribution

T3 - Acta Mathematica Universitatis Comenianae

SP - 507

EP - 510

BT - Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019)

ER -