Decomposition of complete bipartite graphs into generalized prisms

Abstract

R. Häggkvist proved that every 3-regular bipartite graph of order 2n with no component isomorphic to the Heawood graph decomposes the complete bipartite graph K6n,6n. In (Cichacz and Fronček, 2009) [2] the first two authors established a necessary and sufficient condition for the existence of a factorization of the complete bipartite graph Kn,n into certain families of 3-regular graphs of order 2n. In this paper we tackle the problem of decompositions of Kn,n into certain 3-regular graphs called generalized prisms. We will show that certain families of 3-regular graphs of order 2n decompose the complete bipartite graph K3n2,3n2.