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ArticleOriginal scientific text

Title

Decompositions of nearly complete digraphs into t isomorphic parts

Authors 1, 1

Affiliations

  1. Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland

Abstract

An arc decomposition of the complete digraph Kₙ 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 ( Kₙ-R)/t and the ceiling tth class ( Kₙ+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 Kₙ into cycles ^{→}Cn-1 and into paths ^{→}Pₙ is characterized.

Keywords

ENG
decomposition, cyclically 1-generated, remainder, surplus, universal part

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Discussiones Mathematicae Graph Theory
2009/29/3
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Pages:
563-572
Main language of publication
English
Received
2008-05-08
Accepted
2008-09-22
Published
2009

DOI: 10.7151/dmgt.1464

Exact and natural sciences