Orthogonally Resolvable Matching Designs

2017/07/19 by Danziger, Peter, Park, Sophia
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.06317

Abstract

An Orthogonally resolvable Matching Design OMD(n, k) is a partition of the edges the complete graph K_n into matchings of size k, called blocks, such that the blocks can be resolved in two different ways. Such a design can be represented as a square array whose cells are either empty or contain a matching of size k, where every vertex appears exactly once in each row and column. In this paper we show that an OMD(n.k) exists if and only if n ≡ 0 \pmod2k except when k=1 and n = 4 or 6.

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