Geodesic
Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 241-249.

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

It has been shown [3] that any bipartite graph K_a,b, where a, b are even integers, can be decomposed into closed trails with prescribed even lengths. In this article, we consider the corresponding question for directed bipartite graphs. We show that a complete directed bipartite graph ^↔ K_a,b is decomposable into directed closed trails of even lengths greater than 2, whenever these lengths sum up to the size of the digraph. We use this result to prove that complete bipartite multigraphs can be decomposed in a similar manner.
Keywords: trail, decomposition 
@article{DMGT_2007_27_2_a2,
     author = {Cichacz, Sylwia},
     title = {Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {241--249},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a2/}
}
TY  - JOUR
AU  - Cichacz, Sylwia
TI  - Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 241
EP  - 249
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a2/
LA  - en
ID  - DMGT_2007_27_2_a2
ER  - 
%0 Journal Article
%A Cichacz, Sylwia
%T Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 241-249
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a2/
%G en
%F DMGT_2007_27_2_a2
Cichacz, Sylwia. Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 241-249. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a2/

[1] P.N. Balister, Packing Circuits into Kₙ, Combin. Probab. Comput. 10 (2001) 463-499, doi: 10.1017/S0963548301004771.

[2] P.N. Balister, Packing digraphs with directed closed trails, Combin. Probab. Comput. 12 (2003) 1-15, doi: 10.1017/S0963548302005461.

[3] M. Hornák and M. Woźniak, Decomposition of complete bipartite even graphs into closed trails, Czechoslovak Math. J. 128 (2003) 127-134.