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

Voir la notice de l'article provenant de la source Library of Science

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 
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/
@article{DMGT_2017_37_1_a4,
     author = {Froncek, Dalibor},
     title = {Decomposition of {Certain} {Complete} {Bipartite} {Graphs} into {Prisms}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {55--62},
     year = {2017},
     volume = {37},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a4/}
}
TY  - JOUR
AU  - Froncek, Dalibor
TI  - Decomposition of Certain Complete Bipartite Graphs into Prisms
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2017
SP  - 55
EP  - 62
VL  - 37
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a4/
LA  - en
ID  - DMGT_2017_37_1_a4
ER  - 
%0 Journal Article
%A Froncek, Dalibor
%T Decomposition of Certain Complete Bipartite Graphs into Prisms
%J Discussiones Mathematicae. Graph Theory
%D 2017
%P 55-62
%V 37
%N 1
%U http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a4/
%G en
%F DMGT_2017_37_1_a4

[1] S. Cichacz and D. Fronček, Factorization of Kn,n into (0, j)-prisms, Inform. Process. Lett. 109 (2009) 932–934. doi:10.1016/j.ipl.2009.04.024

[2] S. Cichacz, D. Fronček and P. Kovář, Note on decomposition of Kn,n into (0, j)-prisms, Lect. Notes in Comput. Sci. 5874 (2009) 125–133. doi:10.1007/978-3-642-10217-2_15

[3] S. Cichacz, D. Fronček and P. Kovář, Decomposition of complete bipartite graphs into generalized prisms, European J. Combin. 34 (2013) 104–110. doi:10.1016/j.ejc.2012.07.018

[4] D. Froncek, Product rosy labeling, Discuss. Math. Graph Theory 28 (2008) 431–440. doi:10.7151/dmgt.1417

[5] R.W. Frucht and J.A. Gallian, Labelling prisms, Ars Combin. 26 (1988) 69–82.

[6] R. Häggkvist, Decompositions of complete bipartite graphs, Surveys in Combinatorics, 1989 (Norwich, 1989), 115–147, London Math. Soc. Lecture Note Ser. 141 (Cambridge Univ. Press, Cambridge, 1989).

[7] A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs, Internat. Symposium, Rome, July 1966 (Gordon and Breach, N.Y. and Dunod, Paris, 1967) 349–355.