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Discussiones Mathematicae Graph Theory 29(3) (2009) 563-572
DOI: https://doi.org/10.7151/dmgt.1464

DECOMPOSITIONS OF NEARLY COMPLETE DIGRAPHS INTO t ISOMORPHIC PARTS

Mariusz Meszka  and  Zdzisław Skupień

Faculty of Applied Mathematics
AGH University of Science and Technology
al. Mickiewicza 30, 30-059 Kraków, Poland
e-mail: meszka@agh.edu.pl,  skupien@agh.edu.pl

Abstract

An arc decomposition of the complete digraph 𝒟K_n into t isomorphic subdigraphs is generalized to the case where the numerical divisibility condition is not satisfied. Two sets of nearly tth parts are constructively proved to be nonempty. These are the floor tth class (𝒟K_n-R)/t and the ceiling tth class (𝒟K_n+S)/t, where R and S comprise (possibly copies of) arcs whose number is the smallest possible. The existence of cyclically 1-generated decompositions of 𝒟K_n into cycles C_n−1→ and into paths P_n→ is characterized.

Keywords: decomposition, cyclically 1-generated, remainder, surplus, universal part.

2000 Mathematics Subject Classification: 05C70, 05C20.

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Received 8 May 2008
Revised 22 September 2008
Accepted 13 October 2008