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 paper
T3 - Acta Mathematica Universitatis Comenianae
SP - 507
EP - 510
BT - Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019)
T2 - European Conference on Combinatorics, Graph Theory and Applications
Y2 - 26 August 2019 through 30 August 2019
ER -