Cycle Decompositions of Complete Multigraphs

被引：28

作者：

Bryant, Darryn ^{[1
]}

Horsley, Daniel ^{[2
]}

Maenhaut, Barbara ^{[1
]}

Smith, Benjamin R. ^{[1
]}

机构：

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

[2] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2011年 / 19卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

cycle decomposition; graph decomposition; G-design; COMPLETE GRAPHS; ALSPACH CONJECTURE; K-N; LENGTH;

D O I：

10.1002/jcd.20263

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that the obvious necessary conditions for the existence of a decomposition of the complete multigraph with n vertices and with lambda edges joining each pair of distinct vertices into m-cycles, or into m-cycles and a perfect matching, are also sufficient. This result follows as an easy consequence of more general results which are obtained on decompositions of complete multigraphs into cycles of varying lengths. (C) 2010 Wiley Periodicals, Inc. J Combin Designs 19: 42-69, 2010

引用

页码：42 / 69

页数：28

共 29 条

[1] On Alspach's conjecture with two even cycle lengths [J].