Resolvable tree designs
type: Item
instance of: scholarly article
title: Resolvable tree designs
zbMATH Open document ID: 0769.05079
DOI: 10.1016/0097-3165(92)90027-R
author: Min-Li Yu
published in: Journal of Combinatorial Theory. Series A
publication date: 1993-01-17T00:00:00Z
review text: A graph \(G\) has an \(H\)-factorization \((H| G)\) if the edges of \(G\) can be partitioned into \(H\)-factors (an \(H\)-factor is a spanning subgraph each component of which is isomorphic to \(H\)). Let \(K_ n\) denote the complete graph of order \(n\) where each edge has multiplicity \(\lambda\) and \(T_ k\) be a tree with \(k\) vertices. Main results are \[ \text{If } T_ k| K_ k\text{ then } T_ k|\lambda K_ n\text{ iff } n\equiv 0\pmod k\text{ and } \lambda k(n-1)\equiv 0\pmod{2(k-1)}. \tag{1} \] \[ \text{If } T_ k| 2K_ k\text{ then }T_ k| 2\lambda K_ n\text{ iff } n\equiv 0\pmod k \text{ and }\lambda k(n-1)\equiv 0\pmod{k-1}. \tag{2} \] {}.
reviewed by: Ján Plesník
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 96582
zbMATH Keywords: factorization
zbMATH Keywords: complete graph
zbMATH Keywords: tree
MaRDI profile type: Publication
cites work: Existence of resolvable path designs
cites work: Resolvable path designs
cites work: Q3300165
cites work: Q3208693
cites work: On resolvable tree-decompositions of complete graphs
cites work: Decomposition of a complete multigraph into simple paths: nonbalanced handcuffed designs
cites work: Decomposition of complete multigraphs into stars
cites work: A Hamiltonian decomposition of \(K^*_{2m},2m\geq 8\)
full work available at URL: 0097-3165(92)90027-r
OpenAlex ID: W2048121132
description: scientific article; zbMATH DE number 96582