On judicious partitions of uniform hypergraphs

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:141

Article

Hou, Jianfeng¹  Wu, Shufei¹  Yan, Guiying² 

[1] Fuzhou Univ, Ctr Discrete Math, Fujian 850003, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

关键词: Uniform hypergraph;    Judicious partition;    Azuma-Hoeffding inequality;   

DOI  :  10.1016/j.jcta.2016.02.004

来源: Elsevier

【 摘 要 】

Bollobas and Scott showed that the vertices of a graph of m edges can be partitioned into k sets such that each set contains at most m/k(2) o(m) edges. They conjectured that the vertices of an r-uniform hypergraph, where r > 3, of m edges may likewise be partitioned into k sets such that each set contains at most m/kr o(m) edges. In this paper, we prove the weaker statement that a partition into k sets can be found in which each set contains at most m/(k-1)(r)+r(1/2) +o(m) edges. Some partial results on this conjecture are also given. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free