THE BOLLOBAS SCOTT CONJECTURE FOR 4-UNIFORM HYPERGRAPHS

被引：4

作者：

Hou, Jianfeng ^{[1
]}

Wu, Shufei ^{[1
,2
]}

Zeng, Qinghou ^{[1
,3
]}

Zhu, Wenxing ^{[1
]}

机构：

[1] Fuzhou Univ, Ctr Discrete Math, Fuzhou 350116, Fujian, Peoples R China

[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Henan, Peoples R China

[3] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2018年 / 32卷 / 01期

基金：

中国国家自然科学基金;

关键词：

hypergraph; partition; Azuma-Hoeffding inequality; JUDICIOUS K-PARTITIONS; 3-UNIFORM HYPERGRAPHS; UNIFORM HYPERGRAPHS; GRAPHS; BOUNDS; BISECTIONS; CUT;

D O I：

10.1137/17M1128484

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let r >= 3 and k >= 2 be fixed integers. Bollobas and Scott conjectured that every r-uniform hypergraph with m edges has a vertex partition into k sets with at most m/k(r)+o(m) edges in each set, and proved the conjecture in the case r = 3. In this paper, we confirm this conjecture in the case r = 4 by showing that every 4-uniform hypergraph with m edges has a vertex partition into k sets with at most m/k(4) + O(m(8/9)) edges in each set.

引用

页码：505 / 521

页数：17

共 27 条

[21] ON A BOTTLENECK BIPARTITION CONJECTURE OF ERDOS [J].

PORTER, TD .

COMBINATORICA, 1992, 12 (03) :317-321

[22]

Shahrokhi F., 1994, Journal of Combinatorial Mathematics and Combinatorial Computing, V15, P221

[23] On judicious bisections of graphs [J].

Xu, Baogang ;

Yu, Xingxing .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2014, 106 :30-69

[24] Better Bounds for k-Partitions of Graphs [J].

Xu, Baogang ;

Yu, Xingxing .

COMBINATORICS PROBABILITY & COMPUTING, 2011, 20 (04) :631-640

[25] Judicious k-partitions of graphs [J].

Xu, Baogang ;

Yu, Xingxing .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2009, 99 (02) :324-337

[26]

Yannakakis M., 1978, NODE EDGE DELETION N, P253

[27] On judicious partitions of hypergraphs with edges of size at most 3 [J].

Zhang, Yao ;

Tang, Yu Cong ;

Yan, Gui Ying .

EUROPEAN JOURNAL OF COMBINATORICS, 2015, 49 :232-239

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