Note on Decomposition of K n,n into (0,j)-prisms

Abstract

R. Haggkvist proved that every 3-regular bipartite graph of order 2n with no component isomorphic to the Heawood graph decomposes the complete bipartite graph K 6n,6n . In [2] the first two authors established a necessary and sufficient condition for the existence of a factorization of the complete bipartite graph K n,n into certain families of 3-regular graphs of order 2n. In this paper we tackle the problem of decompositions of K n,n into 3-regular graphs some more. We will show that certain families of 3-regular graphs of order 2n decompose the complete bipartite graph $K_{\frac{3n}{2},\frac{3n}{2}}$.