图中 K9 ${K}_{9}$ 未成数的局部度条件

Pub Date : 2024-05-08 DOI:10.1002/jgt.23110

Takashige Akiyama

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引用次数: 0

摘要

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。

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

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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