关于berge环的Gyárfás, Lehel, Sárközy和Schelp猜想的证明

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Combinatorics, Probability & Computing Pub Date : 2021-03-09 DOI:10.1017/S0963548320000243

G. Omidi

引用次数: 5

摘要

我们已经推测，对于任意固定的\[{\text{r}} \geqslant 2\]和足够大的n，在n个顶点上的完全r-均匀超图\[{\text{K}}_{\text{n}}^{\text{r}}\]的每一个\[({\text{r}} - 1)\] -色边中都存在一个单色哈密顿berge环。本文证明了这一猜想。

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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A proof of a conjecture of Gyárfás, Lehel, Sárközy and Schelp on Berge-cycles

It has been conjectured that, for any fixed

\[{\text{r}} \geqslant 2\]

and sufficiently large n, there is a monochromatic Hamiltonian Berge-cycle in every

\[({\text{r}} - 1)\]

-colouring of the edges of

\[{\text{K}}_{\text{n}}^{\text{r}}\]

, the complete r-uniform hypergraph on n vertices. In this paper we prove this conjecture.

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来源期刊

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.

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