在四连通图中，与顶点的度数大于4的边和可收缩边数的下界相关联的边

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.005

Shunsuke Nakamura, Yoshimi Egawa, Keiko Kotani

引用次数: 0

摘要

本文证明了4连通图G的4可收缩边(收缩后不改变初始图连通性的边)的个数至少为(1/28)∑x∈V≥5(G)degG (x)，其中V≥5(G)表示G的度大于或等于5的顶点的集合。这是对Ando等人证明的结果的改进。[关于4连通图中4可收缩边的数量，J. Combin。]Ser的理论。B . 99(2009): 97-109。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Edges incident with a vertex of degree greater than four and a lower bound on the number of contractible edges in a 4-connected graph

In this paper, we prove that the number of 4-contractible edges (edges that after contraction do not change the connectivity of the initial graph) of a 4-connected graph G is at least $(1 / 28) \sum_{x \in V_{\geq 5} (G)} \deg_{G} (x)$ , where $V_{\geq 5} (G)$ denotes the set of those vertices of G which have degree greater than or equal to 5.

This is the refinement of the result proved by Ando et al. [On the number of 4-contractible edges in 4-connected graphs, J. Combin. Theory Ser. B 99 (2009) 97–109].

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.