On tight 9-cycle decompositions of complete 3-uniform hypergraphs

被引：0
|
作者：
Bunge, Ryan C. [1 ]
Darrow, Brian D., Jr. [2 ]
El-Zanati, Saad, I [1 ]
Hadaway, Kimberly P. [3 ]
Pryor, Megan K. [4 ]
Romer, Alexander J. [5 ]
Squires, Alexandra [6 ]
Stover, Anna C. [7 ]
机构：
[1] Illinois State Univ, Normal, IL 61761 USA
[2] Columbia Univ, New York, NY USA
[3] Williams Coll, Williamstown, MA 01267 USA
[4] North Carolina State Univ, Raleigh, NC USA
[5] Millikin Univ, Decatur, IL USA
[6] Lee Univ, Cleveland, TN USA
[7] Grand Valley State Univ, Allendale, MI 49401 USA
来源：
AUSTRALASIAN JOURNAL OF COMBINATORICS | 2021年 / 80卷
基金：
美国国家科学基金会;
关键词：
CYCLE DECOMPOSITIONS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The complete 3-uniform hypergraph of order v, denoted by K-v((3)), has a set V of size v as its vertex set and the set of all 3-element subsets of V as its edge set. A 3-uniform tight 9-cycle has vertex set {v(1), v(2), v(3), v(4), v(5), v(6), v(7), v(8), v(9)} and edge set { {v(1), v(2), v(3)}, {v(2), v(3), v(4)}, {v(3), v(4), v(5)}, {v(4), v(5), v(6)}, {v(5), v(6), v(7)}, {v(6), v(7), v(8)}, {v(7), v(8), v(9)}, {v(8), v(9), v(1)}, {v(9), v(1), v(2)}}. We show there exists a tight 9-cycle decomposition of K-v((3)) if and only if v equivalent to 1 or 2 (mod 27).
引用
收藏
页码：233 / 240
页数：8
相关论文
共 50 条
  • [41] LOCALISED CODEGREE CONDITIONS FOR TIGHT HAMILTONIAN CYCLES IN 3-UNIFORM HYPERGRAPHS
    Araujo, P.
    Piga, S.
    Schacht, M.
    ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2019, 88 (03): : 389 - 394
  • [42] Prime 3-Uniform Hypergraphs
    Abderrahim Boussaïri
    Brahim Chergui
    Pierre Ille
    Mohamed Zaidi
    Graphs and Combinatorics, 2021, 37 : 2737 - 2760
  • [43] Matchings in 3-uniform hypergraphs
    Kuehn, Daniela
    Osthus, Deryk
    Treglown, Andrew
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2013, 103 (02) : 291 - 305
  • [44] Large monochromatic components in colorings of complete 3-uniform hypergraphs
    Gyarfas, Andras
    Haxell, Penny
    DISCRETE MATHEMATICS, 2009, 309 (10) : 3156 - 3160
  • [45] Partitioning 3-uniform hypergraphs
    Ma, Jie
    Yu, Xingxing
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2012, 102 (01) : 212 - 232
  • [46] Wickets in 3-uniform hypergraphs
    Solymosi, Jozsef
    DISCRETE MATHEMATICS, 2024, 347 (06)
  • [47] Matching in 3-uniform hypergraphs
    Zhang, Yi
    Lu, Mei
    DISCRETE MATHEMATICS, 2019, 342 (06) : 1731 - 1737
  • [48] Decompositions of λ-fold complete bipartite 3-uniform hypergraphs λKn,n(3) into hypergraph K4(3) - e
    Zhao, Hongtao
    Zhang, Qingyun
    UTILITAS MATHEMATICA, 2020, 115 : 227 - 237
  • [49] Almost partitioning 2-colored complete 3-uniform hypergraphs into two monochromatic tight or loose cycles
    Bustamante, Sebastian
    Han, Hiep
    Stein, Maya
    JOURNAL OF GRAPH THEORY, 2019, 91 (01) : 5 - 15
  • [50] Turán Numbers of Complete 3-Uniform Berge-Hypergraphs
    L. Maherani
    M. Shahsiah
    Graphs and Combinatorics, 2018, 34 : 619 - 632
12345