Local degree conditions for K 9 ${K}_{9}$ -minors in graphs

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-05-08 DOI:10.1002/jgt.23110

Takashige Akiyama

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引用次数: 0

Abstract

We prove that if each edge of a graph $G$ belongs to at least seven triangles, then $G$ contains a $K_{9}$ -minor or contains $K_{1, 2, 2, 2, 2, 2}$ as an induced subgraph. This result was conjectured by Albar and Gonçalves in 2018. Moreover, we apply this result to study the stress freeness of graphs.

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图中 K9 ${K}_{9}$ 未成数的局部度条件

我们证明，如果一个图的每条边至少属于七个三角形，那么就包含一个-小图或包含一个诱导子图。这一结果是阿尔巴和贡萨尔维斯在 2018 年猜想出来的。此外，我们还将这一结果应用于研究图的应力自由性。

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

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 .