Maximum vertex and face degree of oblique graphs
Abstract
Let G = ( V , E , F ) be a 3-connected simple graph imbedded into a surface S with vertex set V, edge set E and face set F. A face α is an a1, a2, ... , ak-face if α is a k-gon and the degrees of the vertices incident with α in the cyclic order are a1, a2, ... , ak. The lexicographic minimum b1, b2, ... , bk such that α is a b1, b2, ... , bk-face is called the type of α. Let z be an integer. We consider z-oblique graphs, i.e. such graphs that the number of faces of each type is at most z. We show an upper bound for the maximum vertex degree of any z-oblique graph imbedded into a given surface. Moreover, an upper bound for the maximum face degree is presented. We also show that there are only finitely many oblique graphs imbedded into non-orientable surfaces.
Domains
Discrete Mathematics [cs.DM]
Origin : Files produced by the author(s)
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