没有给定长度的Berge路径的线性三均匀超图

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2024-12-05 DOI:10.1016/j.jctb.2024.11.003

Ervin Győri , Nika Salia

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引用次数: 0

摘要

研究了Erdős-Gallai定理在一般超图中的推广。本文证明了线性超图Erdős-Gallai定理的推广。特别地，我们证明了在一个n顶点3-一致线性超图中，当k≥4时，不存在长度为k的Berge路径作为子图时，超边的数目最多为（k−1）6n。对于无穷多个k和n，边界很明显。

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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Linear three-uniform hypergraphs with no Berge path of given length

Extensions of Erdős-Gallai Theorem for general hypergraphs are well studied. In this work, we prove the extension of Erdős-Gallai Theorem for linear hypergraphs. In particular, we show that the number of hyperedges in an n-vertex 3-uniform linear hypergraph, without a Berge path of length k as a subgraph is at most

\frac{(k - 1)}{6} n

for

k \geq 4

. The bound is sharp for infinitely many k and n.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.