Star-factorization of symmetric complete bipartite multi-digraphs
type: Item
instance of: scholarly article
title: Star-factorization of symmetric complete bipartite multi-digraphs
zbMATH Open document ID: 0946.05066
DOI: 10.1016/S0012-365X(99)00321-0
author: Kazuhiko Ushio
published in: Discrete Mathematics
publication date: 2000-10-18T00:00:00Z
review text: The symmetric complete bipartite multi-digraph \(\lambda K^{*}_{m,n}\) is the symmetric complete bipartite digraph \(K^{*}_{m,n}\) in which every arc is taken \(\lambda\) times. For \(k\geq 3\) let \(S_k\) be the orientation of the star \(K_{1,k-1}\) such that every arc in \(S_k\) is directed from the center vertex towards leaves. It is shown that \(\lambda K^{*}_{m,n}\) is the union of arc-disjoint \(S_k\) if and only if \(m=n\equiv 0\pmod {k (k-1)/d}\), where \(d=(\lambda, k-1)\).
reviewed by: Fedor V. Fomin
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 1439842
zbMATH Keywords: star-facrorization
zbMATH Keywords: symmetric complete bipartite multi-graph
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00321-0
OpenAlex ID: W1972221471
description: scientific article; zbMATH DE number 1439842