Monochromatic loose path partitions in k-uniform hypergraphs

Changhong Lu; Bing Wang; Ping Zhang

doi:10.1016/j.disc.2017.08.018

Monochromatic loose path partitions in k-uniform hypergraphs

Changhong Lu
, Bing Wang^*
, Ping Zhang

^*此作品的通讯作者

数学科学学院

Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice
East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

A conjecture of Gyárfás and Sárközy says that in every 2-coloring of the edges of the complete k-uniform hypergraph K_n^k, there are two disjoint monochromatic loose paths of distinct colors such that they cover all but at most k−2 vertices. A weaker form of this conjecture with 2k−5 uncovered vertices instead of k−2 is proved. Thus the conjecture holds for k=3. The main result of this paper states that the conjecture is true for all k≥3.

源语言	英语
页（从-至）	2789-2791
页数	3
期刊	Discrete Mathematics
卷	340
期	12
DOI	https://doi.org/10.1016/j.disc.2017.08.018
出版状态	已出版 - 12月 2017

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title = "Monochromatic loose path partitions in k-uniform hypergraphs",

abstract = "A conjecture of Gy{\'a}rf{\'a}s and S{\'a}rk{\"o}zy says that in every 2-coloring of the edges of the complete k-uniform hypergraph Knk, there are two disjoint monochromatic loose paths of distinct colors such that they cover all but at most k−2 vertices. A weaker form of this conjecture with 2k−5 uncovered vertices instead of k−2 is proved. Thus the conjecture holds for k=3. The main result of this paper states that the conjecture is true for all k≥3.",

keywords = "Colored complete uniform hypergraphs, Monochromatic loose path, Partition",

author = "Changhong Lu and Bing Wang and Ping Zhang",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

month = dec,

doi = "10.1016/j.disc.2017.08.018",

language = "英语",

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T1 - Monochromatic loose path partitions in k-uniform hypergraphs

AU - Lu, Changhong

AU - Wang, Bing

AU - Zhang, Ping

PY - 2017/12

Y1 - 2017/12

N2 - A conjecture of Gyárfás and Sárközy says that in every 2-coloring of the edges of the complete k-uniform hypergraph Knk, there are two disjoint monochromatic loose paths of distinct colors such that they cover all but at most k−2 vertices. A weaker form of this conjecture with 2k−5 uncovered vertices instead of k−2 is proved. Thus the conjecture holds for k=3. The main result of this paper states that the conjecture is true for all k≥3.

AB - A conjecture of Gyárfás and Sárközy says that in every 2-coloring of the edges of the complete k-uniform hypergraph Knk, there are two disjoint monochromatic loose paths of distinct colors such that they cover all but at most k−2 vertices. A weaker form of this conjecture with 2k−5 uncovered vertices instead of k−2 is proved. Thus the conjecture holds for k=3. The main result of this paper states that the conjecture is true for all k≥3.

KW - Colored complete uniform hypergraphs

KW - Monochromatic loose path

KW - Partition

UR - https://www.scopus.com/pages/publications/85028765733

U2 - 10.1016/j.disc.2017.08.018

DO - 10.1016/j.disc.2017.08.018

M3 - 文章

AN - SCOPUS:85028765733

SN - 0012-365X

VL - 340

SP - 2789

EP - 2791

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 12

ER -

Monochromatic loose path partitions in k-uniform hypergraphs

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