It is well known that if n is even, the addition table for the integersmodulo n (whichwe denote by Bn) possesses no transversals.We show that ifn is odd, then the number of transversals in Bn is at… (More)

Necessary and su1⁄2cient conditions for the existence of an edge-disjoint decomposition of any complete multipartite graph into even length cycles are investigated. Necessary conditions are listed… (More)

If a graph G decomposes into edge-disjoint 4-cycles, then each vertex of G has even degree and 4 divides the number of edges in G. It is shown that these obvious necessary conditions are also… (More)

Let L be chosen uniformly at random from among the latin squares of order n ≥ 4 and let r, s be arbitrary distinct rows of L. We study the distribution of σr,s, the permutation of the symbols of L… (More)

We show that a complete tripartite graph with three partite sets of equal size m may be decomposed into k-cycles for any k 2: 3 if and only if k divides 3m2 and k ::; 3m.

For a finite triangulation of the plane with faces properly coloured white and black, let AW be the abelian group constructed by labelling the vertices with commuting indeterminates and adding… (More)