Decompositions into 2-regular subgraphs and equitable partial cycle decompositions

Darryn Bryant, Daniel Horsley, Barbara Maenhaut

Research output: Contribution to journalArticleResearchpeer-review

19 Citations (Scopus)

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,..., mt if and only if n is odd, 3a??mia??n for i = 1, 2,..., t, and m1 + m2 + ... + mt = (n/2). 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,..., mt, then there exists an equitable partial decomposition of K n into t cycles of lengths m1, m2,..., 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
Original languageEnglish
Pages (from-to)67 - 72
Number of pages6
JournalJournal of Combinatorial Theory, Series B
Volume93
Issue number1
DOIs
Publication statusPublished - 2005
Externally publishedYes

Cite this