Turkish Journal of Mathematics
Abstract
This paper investigates the maximum genus and upper embeddability of connected 4-regular graphs. We obtain lower bounds on the maximum genus of connected 4-regular simple graphs and connected 4-regular graphs without loops in terms of the Betti number. The definition of the Betti number is referred to [Gross and Tucker, Topological Graph Theory, New York, 1987]. Furthermore, we give examples that show that these lower bounds are tight.
DOI
10.3906/mat-0912-19
Keywords
Maximum genus, upper embeddable, Betti number
First Page
530
Last Page
537
Recommended Citation
ZHOU, D, HAO, R, & HE, W (2012). Lower bounds for the maximum genus of 4-regular graphs. Turkish Journal of Mathematics 36 (4): 530-537. https://doi.org/10.3906/mat-0912-19
