Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516215 | Journal of Combinatorial Theory, Series B | 2005 | 6 Pages |
Abstract
Two theorems are proved in this paper. Firstly, it is proved that there exists a decomposition of the complete graph of order n into t edge-disjoint 2-regular subgraphs of orders m1,m2,â¦,mt if and only if n is odd, 3⩽mi⩽n for i=1,2,â¦,t, and m1+m2+â¦+mt=n2. Secondly, it is proved that if there exists partial decomposition of the complete graph Kn of order n into t cycles of lengths m1,m2,â¦,mt, then there exists an equitable partial decomposition of Kn into t cycles of lengths m1,m2,â¦,mt. A decomposition into cycles is equitable if for any two vertices u and v, the number of cycles containing u and the number of cycles containing v differ by at most 1.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Darryn Bryant, Daniel Horsley, Barbara Maenhaut,