Maximum uniformly resolvable decompositions of Kv and Kv−I into 3-stars and 3-cycles

doi:10.1016/j.disc.2014.05.016

Discrete Mathematics

Volume 338, Issue 10, 6 October 2015, Pages 1667-1673

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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.

Keywords

Resolvable graph decomposition

Uniform resolutions

Paths

3-stars