超图厄尔多斯-加莱定理的本地化版本

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-18 DOI:10.1016/j.disc.2024.114293

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引用次数: 0

摘要

在 n 个顶点的均匀超图 H 中，边的权函数是根据包含该边的最长 Berge 路径中的边数定义的。我们证明了 H 中所有边的权函数值之和最多为 n，并描述了达到这一界限的所有极值超图的特征。这一结果加强并扩展了经典厄尔多斯-加莱定理的超图版本，提供了该定理的局部版本。

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Localized version of hypergraph Erdős-Gallai Theorem

The weight function of an edge in an n-vertex uniform hypergraph

H

is defined with respect to the number of edges in the longest Berge path containing the edge. We prove that the summation of the weight function values for all edges in

H

is at most n, and characterize all extremal hypergraphs that attain this bound. This result strengthens and extends the hypergraph version of the classic Erdős-Gallai Theorem, providing a local version of this theorem.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.