最小度$4$的线性$3$图中的冠

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2022-10-21 DOI:10.37236/11037

Alvaro Carbonero, Willem Fletcher, Jing Guo, A. Gyárfás, Rona Wang, Shiyu Yan

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引用次数: 0

摘要

3-图是集合的一对H = (V, E)，其中V的元素称为点或顶点，E包含V的一些3元素子集，称为边。如果任意两条不同的边相交于至多一个顶点，则称为线性3-图。最近，人们对3图的极值性质产生了兴趣，3图包含无冠、三条不相交的边和与所有边相交的第四条边。我们证明了每一个最小度为4的线性3图都包含一个冠。如果4被3代替，这就不成立了。

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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Crowns in Linear $3$-Graphs of Minimum Degree $4$

A 3-graph is a pair H = (V, E) of sets, where elements of V are called points or vertices and E contains some 3-element subsets of V , called edges. A 3-graph is called linear if any two distinct edges intersect in at most one vertex.There is a recent interest in extremal properties of 3-graphs containing no crown, three pairwise disjoint edges and a fourth edge which intersects all of them. We show that every linear 3-graph with minimum degree 4 contains a crown. This is not true if 4 is replaced by 3.

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.