Maximum genus, connectivity and minimal degree of graphs Original Research Article

This paper is devoted to the lower bounds on the maximum genus of graphs. A simple statement of our results in this paper can be expressed in the following form: Let G be a k-edge-connected graph with minimum degree image, for each positive integer image, there exists a non-decreasing function image such that the maximum genus image of G satisfies the relation image, and furthermore that image, where image is the cycle rank of G. The result shows that lower bounds of the maximum genus of graphs with any given connectivity become larger and larger as their minimum degree increases, and complements recent results of several authors.