Bounding the cop number of a graph by its genus

Nathan Bowler, Joshua Erde, Florian Lehner, Max Pitz

Research output: Contribution to journalArticlepeer-review

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 $g(G)$. The best known bound, that $c(G) \leq \left\lfloor \frac{3 g(G)}{2}\right\rfloor + 3$, was given by Schr\"{o}der, who conjectured that in fact $c(G) \leq g(G) + 3$. We give the first improvement to Schr\"{o}der's bound, showing that $c(G) \leq \frac{4g(G)}{3} + \frac{10}{3}$.
Original language English 2459-2489 31 SIAM Journal on Discrete Mathematics 35 4 https://doi.org/10.1137/20M1312150 Published - 19 Nov 2021

Keywords

• cops and robbers
• surfaces

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