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Turkish Journal of Mathematics

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.

First Page

530

Last Page

537

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