k-Uniform 超图中的循环分解

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2024-03-05 DOI:10.1016/j.jctb.2024.02.003

Allan Lo , Simón Piga , Nicolás Sanhueza-Matamala

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引用次数: 0

摘要

我们证明，n 个顶点上的 k 个均匀超图，如果其码度至少为 (2/3+o(1))n，则可以分解为紧密循环，但必须满足微不足道的可分条件。作为推论，我们证明这些图也包含紧密欧拉游。此外，我们还证明了为任意 k-uniform 超图的边分解建立吸收器的另一个条件，这应该是独立的兴趣所在。

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Cycle decompositions in k-uniform hypergraphs

We show that k-uniform hypergraphs on n vertices whose codegree is at least $(2 / 3 + o (1)) n$ can be decomposed into tight cycles, subject to the trivial divisibility conditions. As a corollary, we show those graphs contain tight Euler tours as well. In passing, we also investigate decompositions into tight paths.

In addition, we also prove an alternative condition for building absorbers for edge-decompositions of arbitrary k-uniform hypergraphs, which should be of independent interest.

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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.