A Cyclic Solution for an Infinite Class of Hamilton-Waterloo Problems

被引：14
|
作者：
Buratti, Marco [1 ]
Danziger, Peter [2 ]
机构：
[1] Univ Perugia, Dipartimento Matemat & Informat, Via Vanvitelli 1, I-06123 Perugia, Italy
[2] Ryerson Univ, Dept Math, 350 Victoria St, Toronto, ON M5B 2K3, Canada
来源：
GRAPHS AND COMBINATORICS | 2016年 / 32卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Two-factorization; Waterloo problem; Skolem sequence; Group action; COMPLETE GRAPH; 2-FACTORIZATIONS; SYSTEMS;
D O I：
10.1007/s00373-015-1582-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main result of this paper is the explicit construction, for any positive integer n, of a cyclic two-factorization of with two-factors consisting of five -cycles and each of the remaining two-factors consisting of all pentagons. Then, applying suitable composition constructions, we obtain a few other two-factorizations also having two-factors of two distinct types.
引用
收藏
页码：521 / 531
页数：11
相关论文
共 50 条
  • [1] A Cyclic Solution for an Infinite Class of Hamilton–Waterloo Problems
    Marco Buratti
    Peter Danziger
    Graphs and Combinatorics, 2016, 32 : 521 - 531
  • [2] On the Hamilton-Waterloo problem
    Adams, P
    Billington, EJ
    Bryant, DE
    El-Zanati, SI
    GRAPHS AND COMBINATORICS, 2002, 18 (01) : 31 - 51
  • [3] On the Hamilton-Waterloo Problem
    Peter Adams
    Elizabeth J. Billington
    Darryn E. Bryant
    Saad I. El-Zanati
    Graphs and Combinatorics, 2002, 18 : 31 - 51
  • [4] On the Hamilton-Waterloo Problem with Odd Orders
    Burgess, A. C.
    Danziger, P.
    Traetta, T.
    JOURNAL OF COMBINATORIAL DESIGNS, 2017, 25 (06) : 258 - 287
  • [5] Octahedral, dicyclic and special linear solutions of some Hamilton-Waterloo problems
    Bonvicini, Simona
    Buratti, Marco
    ARS MATHEMATICA CONTEMPORANEA, 2018, 14 (01) : 1 - 14
  • [6] The Hamilton-Waterloo Problem for Hamilton Cycles and Triangle-Factors
    Lei, Hongchuan
    Shen, Hao
    JOURNAL OF COMBINATORIAL DESIGNS, 2012, 20 (07) : 305 - 316
  • [7] The Hamilton-Waterloo Problem with even cycle lengths
    Burgess, A. C.
    Danziger, P.
    Traetta, T.
    DISCRETE MATHEMATICS, 2019, 342 (08) : 2213 - 2222
  • [8] Infinitely many cyclic solutions to the Hamilton-Waterloo problem with odd length cycles
    Merola, Francesca
    Traetta, Tommaso
    DISCRETE MATHEMATICS, 2016, 339 (09) : 2267 - 2283
  • [9] On the Hamilton-Waterloo problem with odd cycle lengths
    Burgess, A. C.
    Danziger, P.
    Traetta, T.
    JOURNAL OF COMBINATORIAL DESIGNS, 2018, 26 (02) : 51 - 83
  • [10] The Hamilton-Waterloo problem: the case of Hamilton cycles and triangle-factors
    Horak, P
    Nedela, R
    Rosa, A
    DISCRETE MATHEMATICS, 2004, 284 (1-3) : 181 - 188
12345