On the Hamilton-Waterloo Problem for Bipartite 2-Factors

被引：21

作者：

Bryant, Darryn ^{[1
]}

Danziger, Peter ^{[2
]}

Dean, Matthew ^{[1
]}

机构：

[1] Univ Queensland, Dept Math, Brisbane, Qld 4072, Australia

[2] Ryerson Univ, Dept Math, Toronto, ON M5B 2K3, Canada

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2013年 / 21卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

graph decomposition; 2-factorization; graph factorization; Hamilton-Waterloo problem; OBERWOLFACH-PROBLEM; CYCLIC SOLUTIONS; 2-FACTORIZATIONS; GRAPHS; FACTORIZATIONS; DECOMPOSITION;

D O I：

10.1002/jcd.21312

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given two 2-regular graphs F1 and F2, both of order n, the Hamilton-Waterloo Problem for F1 and F2 asks for a factorization of the complete graph Kn into a1 copies of F1, a2 copies of F2, and a 1-factor if n is even, for all nonnegative integers a1 and a2 satisfying a1+a2=?n-12?. We settle the Hamilton-Waterloo Problem for all bipartite 2-regular graphs F1 and F2 where F1 can be obtained from F2 by replacing each cycle with a bipartite 2-regular graph of the same order.

引用

页码：60 / 80

页数：21

共 50 条

[1] On the Hamilton-Waterloo problem
Adams, P
Billington, EJ
Bryant, DE
El-Zanati, SI
GRAPHS AND COMBINATORICS, 2002, 18 (01) : 31 - 51
[2] On the Hamilton-Waterloo Problem
Peter Adams
Elizabeth J. Billington
Darryn E. Bryant
Saad I. El-Zanati
Graphs and Combinatorics, 2002, 18 : 31 - 51
[3] The Hamilton-Waterloo Problem for Hamilton Cycles and Triangle-Factors
Lei, Hongchuan
Shen, Hao
JOURNAL OF COMBINATORIAL DESIGNS, 2012, 20 (07) : 305 - 316
[4] The Hamilton-Waterloo problem for two even cycles factors
Fu, Hung-Lin
Huang, Kuo-Ching
TAIWANESE JOURNAL OF MATHEMATICS, 2008, 12 (04): : 933 - 940
[5] 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
[6] The Hamilton-Waterloo Problem with C4 and Cm factors
Odabsi, Ugur
Ozkan, Sibel
DISCRETE MATHEMATICS, 2016, 339 (01) : 263 - 269
[7] On the Hamilton-Waterloo Problem with Odd Orders
Burgess, A. C.
Danziger, P.
Traetta, T.
JOURNAL OF COMBINATORIAL DESIGNS, 2017, 25 (06) : 258 - 287
[8] The Hamilton-Waterloo Problem for Triangle-Factors and Heptagon-Factors
Lei, Hongchuan
Fu, Hung-Lin
GRAPHS AND COMBINATORICS, 2016, 32 (01) : 271 - 278
[9] The Hamilton-Waterloo problem for Hamilton cycles and C4k-factors
Lei, Hongchuan
Fu, Hung-Lin
Shen, Hao
ARS COMBINATORIA, 2011, 100 : 341 - 348
[10] The Hamilton-Waterloo Problem: The Case of Triangle-Factors and One Hamilton Cycle
Dinitz, J. H.
Ling, Alan C. H.
JOURNAL OF COMBINATORIAL DESIGNS, 2009, 17 (02) : 160 - 176

← 1 2 3 4 5 →