RAINBOW PERFECT MATCHINGS FOR 4-UNIFORM HYPERGRAPHS

被引：4

作者：

Hongliang, Lu ^{[1
]}

Yan, Wang ^{[2
]}

Xingxing, Yu ^{[3
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

[2] Shanghai Jiao Tong Univ, Sch Math Sci, CMA Shanghai, Shanghai 200240, Peoples R China

[3] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2022年 / 36卷 / 03期

基金：

中国国家自然科学基金;

关键词：

rainbow matching; perfect matching; hypergraph; absorbing method; KO-RADO THEOREM; UNIFORM HYPERGRAPHS; ERDOS; SIZE;

D O I：

10.1137/21M1442383

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let n be a sufficiently large integer with n equivalent to 0 (mod 4), and let F-i subset of ((4) ([n])), where i is an element of[n/4]. We show that if each vertex of F-i is contained in more than ((3) (n - 13)) \bigl((3) (3n/4)) edges, then {F-1,..., F-n/4} admits a rainbow matching, i.e., a set of n/4 edges consisting of one edge from each F-i. This generalizes a deep result of Khan J. Combin. Theory Ser. B, 116 (2016), pp. 333-366. on perfect matchings in 4-uniform hypergraphs.

引用

页码：1645 / 1662

页数：18

共 38 条

[1] Aharoni R., SIZE CONDITIONS EXIS
[2] A Rainbow r-Partite Version of the Erdos-Ko-Rado Theorem
Aharoni, Ron
Howard, David
[J]. COMBINATORICS PROBABILITY & COMPUTING, 2017, 26 (03) : 321 - 337
[3] Aharoni R, 2009, ELECTRON J COMB, V16
[4] ON THE SIZE OF GRAPHS WITH COMPLETE-FACTORS
AKIYAMA, J
FRANKL, P
[J]. JOURNAL OF GRAPH THEORY, 1985, 9 (01) : 197 - 201
[5] ALON N., 2004, PROBABILISTIC METHOD
[6] Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels
Alon, Noga
Frank, Peter
Huang, Hao
Roedl, Vojtech
Rucinski, Andrzej
Sudakov, Benny
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2012, 119 (06) : 1200 - 1215
[7] Nonnegative k-sums, fractional covers, and probability of small deviations
Alon, Noga
Huang, Hao
Sudakov, Benny
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2012, 102 (03) : 784 - 796
[8] Balogh J, 2015, J AM MATH SOC, V28, P669
[9] Erdo P., 1965, ANN U SCI BUDAP, V8, P93
[10] Frankl P., 1985, European J. Combin, V6, P317

← 1 2 3 4 →