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

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

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Abstract

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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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

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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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

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