# Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 2, page 241-249
- ISSN: 2083-5892

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topSylwia Cichacz. "Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails." Discussiones Mathematicae Graph Theory 27.2 (2007): 241-249. <http://eudml.org/doc/270717>.

@article{SylwiaCichacz2007,

abstract = {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.},

author = {Sylwia Cichacz},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {trail; decomposition},

language = {eng},

number = {2},

pages = {241-249},

title = {Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails},

url = {http://eudml.org/doc/270717},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Sylwia Cichacz

TI - Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 2

SP - 241

EP - 249

AB - 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.

LA - eng

KW - trail; decomposition

UR - http://eudml.org/doc/270717

ER -

## References

top- [1] P.N. Balister, Packing Circuits into Kₙ, Combin. Probab. Comput. 10 (2001) 463-499, doi: 10.1017/S0963548301004771. Zbl1113.05309
- [2] P.N. Balister, Packing digraphs with directed closed trails, Combin. Probab. Comput. 12 (2003) 1-15, doi: 10.1017/S0963548302005461. Zbl1015.05072
- [3] M. Hornák and M. Woźniak, Decomposition of complete bipartite even graphs into closed trails, Czechoslovak Math. J. 128 (2003) 127-134. Zbl1010.05054