Further results concerning p-quasigroups and complete graph decompositions

Cycle decompositions of the complete graph

For a positive integer n, let G be Kn if n is odd and Kn less a one-factor if n is even. In this paper it is shown that, for non-negative integers p, q and r, there is a decomposition of G into p 4-cycles, q 6-cycles and r 8-cycles if 4p+6q+8r = |E(G)|, q = 0 if n < 6 and r = 0 if n < 8.

Symmetric Bowtie Decompositions of the Complete Graph

Given a bowtie decomposition of the complete graph Kv admitting an automorphism group G acting transitively on the vertices of the graph, we give necessary conditions involving the rank of the group and the cycle types of the permutations in G. These conditions yield non–existence results for instance when G is the dihedral group of order 2v, with v ≡ 1, 9 (mod 12), or a group acting transitive...

Further decompositions of complete tripartite graphs into 5-cycles

Varieties of P-quasigroups

Decompositions of complete undirected graphs into sets of closed trails which partition the edge set of the graph and which contain each pair of distinct vertices exactly once at distance 2 define and are defined by a class of quasigroups called P-quasigroups. Conditions are established under which P-quasigroups are (or are not) homomorphic images of P-quasigroups which possess certain properti...

Lambda-fold complete graph decompositions into perfect four-triple configurations