Maximum uniformly resolvable decompositions of K-v and K-v - I into 3-stars and 3-cycles

Abstract

Let K-v denote the complete graph of order v and K-v - I denote K-v minus a 1-factor. In this article we investigate uniformly resolvable decompositions of K-v and K-v - I into r classes containing only copies of 3-stars and s classes containing only copies of 3-cycles. We completely determine the spectrum in the case where the number of resolution classes of 3-stars is maximum.