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 K 6n,6n. In (Cichacz and Fronček, 2009)  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 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 K 3n/12,3n/2.
Bibliographical noteFunding Information:
The research for this article was partially supported by the institutional project MSM6198910027 and by the Polish Ministry of Science and Higher Education .