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

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2789-2791
Number of pages	3
Journal	Discrete Mathematics
Volume	340
Issue number	12
DOIs	https://doi.org/10.1016/j.disc.2017.08.018
State	Published - Dec 2017

Keywords

Colored complete uniform hypergraphs
Monochromatic loose path
Partition

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10.1016/j.disc.2017.08.018

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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",

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year = "2017",

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AU - Lu, Changhong

AU - Wang, Bing

AU - Zhang, Ping

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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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Keywords

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