A Remark on the Edge-Bandwidth of Tori

Abstract

The edge-bandwidth of a graph $G$ is the smallest number $b$ for which there exists an injective labeling of $E(G)$ with integers such that the difference between the labels of any pair of adjacent edges is at most $b$. The edge-bandwidth of a torus (a product of two cycles) has been computed within an additive error of $5$. In this paper, we improve the upper bound, reducing the error to $3$.