脸的大小和双连通性

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-07-13 DOI:10.1002/jgt.23277

Gunnar Brinkmann, Kenta Noguchi, Heidi Van den Camp

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引用次数: 0

摘要

对于每个c≥1，我们证明了在c连通地图的简单对偶中，必须存在允许1或2切割的面大小的严格下界。利用这些界限，我们确定了c连通映射具有2切简单对偶的最小格，并给出了c连通映射具有a的最小格的下界和上界简单的双刀单切。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Face Sizes and the Connectivity of the Dual

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Face Sizes and the Connectivity of the Dual

For each $c \geq 1$ , we prove tight lower bounds on face sizes that must be present to allow 1- or 2-cuts in simple duals of $c$ -connected maps. Using these bounds, we determine the smallest genus on which a $c$ -connected map can have a simple dual with a 2-cut and give lower and some upper bounds for the smallest genus on which a $c$ -connected map can have a simple dual with a 1-cut.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .