Discussiones Mathematicae Graph Theory 27(2) (2007) 241-249
doi: 10.7151/dmgt.1358

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DECOMPOSITION OF COMPLETE BIPARTITE DIGRAPHS AND EVEN COMPLETE BIPARTITE MULTIGRAPHS INTO CLOSED TRAILS

Sylwia Cichacz

AGH University of Science and Technology
Al. Mickiewicza 30, 30-059 Kraków, Poland
e-mail: cichacz@wms.mat.agh.edu.pl

Abstract

It has been shown [3] that any bipartite graph Ka,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 Ka,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.

2000 Mathematics Subject Classification: 05C70.

References

[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.

Received 13 December 2005
Revised 25 January 2007
Accepted 10 April 2007