Opuscula Math. 31, no. 4 (2011), 599-604
http://dx.doi.org/10.7494/OpMath.2011.31.4.599

Opuscula Mathematica

# Open trails in digraphs

Sylwia Cichacz
Agnieszka Görlich

Abstract. It has been shown in [S. Cichacz, A. Görlich, Decomposition of complete bipartite graphs into open trails, Preprint MD 022, (2006)] that any bipartite graph $$K_{a,b}$$, is decomposable into open trails of prescribed even lengths. In this article we consider the corresponding question for directed graphs. We show that the complete directed graphs $$\overleftrightarrow{K}_n$$ and $$\overleftrightarrow{K}_{a,b}$$ are arbitrarily decomposable into directed open trails.

Keywords: trail, graphdecomposition, bipartite graph.

Mathematics Subject Classification: 05C70.

Full text (pdf)

• Sylwia Cichacz
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
• Agnieszka Görlich
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
• Revised: 2010-09-29.
• Accepted: 2010-10-13.