Decomposition of Certain Complete Bipartite Graphs into Prisms

Abstract

Häggkvist [6] 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 [1] Cichacz and Froncek established a necessary and sufficient condition for the existence of a factorization of the complete bipartite graph Kn,n into generalized prisms of order 2n. In [2] and [3] Cichacz, Froncek, and Kovar showed decompositions of K3n/2,3n/2 into generalized prisms of order 2n. In this paper we prove that K6n/5,6n/5 is decomposable into prisms of order 2n when n ≡ 0 (mod 50).

Keywords

• graph decomposition
• bipartite labeling
• 05c70
• 05c78