- Turkish Journal of Mathematics
- Vol: 36 Issue: 4
- Lower bounds for the maximum genus of 4-regular graphs
Lower bounds for the maximum genus of 4-regular graphs
Authors : Ding Zhou, Rongxia Hao, Weili He
Pages : 530-537
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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