Maximum genus, connectivity, and Nebesky's Theorem

被引：0

作者：

Archdeacon, Dan ^{[1
]}

Kotrbcik, Michal ^{[2
]}

Nedela, Roman ^{[3
]}

Skoviera, Martin ^{[2
]}

机构：

[1] Univ Vermont, Dept Math & Stat, Burlington, VT 05405 USA

[2] Comenius Univ, Dept Comp Sci, Bratislava 84248, Slovakia

[3] Slovak Acad Sci, Math Inst, Banska Bystrica 97549, Slovakia

来源：

ARS MATHEMATICA CONTEMPORANEA | 2015年 / 9卷 / 01期

关键词：

Maximum genus; Nebesky's theorem; Betti number; cycle rank; connectivity; GRAPH;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove lower bounds on the maximum genus of a graph in terms of its connectivity and Betti number (cycle rank). These bounds are tight for all possible values of edge-connectivity and vertex-connectivity and for both simple and non-simple graphs. The use of Nebesky's characterization of maximum genus gives us both shorter proofs and a description of extremal graphs. An additional application of our method shows that the maximum genus is almost additive over the edge cuts.

引用

页码：51 / 61

页数：11

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