Lower bounds for the maximum genus of 4-regular graphs

Authors

DING ZHOU
RONGXIA HAO
WEILI HE

DOI

10.3906/mat-0912-19

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.

Keywords

Maximum genus, upper embeddable, Betti number

First Page

530

Last Page

537

Recommended Citation

ZHOU, DING; HAO, RONGXIA; and HE, WEILI (2012) "Lower bounds for the maximum genus of 4-regular graphs," Turkish Journal of Mathematics: Vol. 36: No. 4, Article 3. https://doi.org/10.3906/mat-0912-19
Available at: https://journals.tubitak.gov.tr/math/vol36/iss4/3