Geodesic
Decomposition of Certain Complete Bipartite Graphs into Prisms
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 55-62

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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 
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Froncek, Dalibor. Decomposition of Certain Complete Bipartite Graphs into Prisms. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 55-62. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a4/