TY - JOUR

T1 - Decompositions into 2-regular subgraphs and equitable partial cycle decompositions

AU - Bryant, Darryn

AU - Horsley, Daniel

AU - Maenhaut, Barbara

PY - 2005

Y1 - 2005

N2 - 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

AB - 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

UR - http://www.sciencedirect.com/science/article/pii/S0095895604000620

U2 - 10.1016/j.jctb.2004.06.002

DO - 10.1016/j.jctb.2004.06.002

M3 - Article

SN - 0095-8956

VL - 93

SP - 67

EP - 72

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

IS - 1

ER -