Existence of resolvable path designs
type: Item
instance of: scholarly article
title: Existence of resolvable path designs
zbMATH Open document ID: 0712.05045
DOI: 10.1016/S0195-6698(13)80120-5
author: Katherine Heinrich
author: Min-Li Yu
author: Jean-Claude Bermond
published in: European Journal of Combinatorics
publication date: 1990-01-01T00:00:00Z
review text: Let \(\lambda K_ n\) denote the complete multigraph on n vertices in which every edge has multiplicity \(\lambda\), and let \(P_ k\) denote the path with k vertices. A \(P_ k\)-factor of \(\lambda K_ n\) is a spanning subgraph each component of which is isomorphic to \(P_ k\). The authors prove that the edge set of \(\lambda K_ n\) has a partition into \(P_ k\)-factors, \(k\geq 2\), if and only if \(n\equiv 0(mod k)\) and \(\lambda\) k(n-1)\(\equiv 0(mod 2k-2)\).
reviewed by: Brian Alspach
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 4170950
zbMATH Keywords: factorization
zbMATH Keywords: resolvable
zbMATH Keywords: complete multigraph
zbMATH Keywords: \(P_ k\)-factor
zbMATH Keywords: spanning subgraph
zbMATH Keywords: partition
MaRDI profile type: Publication
cites work: The Oberwolfach problem and factors of uniform odd length cycles
cites work: Q3737429
cites work: Graph decompositions, handcuffed prisoners and balanced p-designs
cites work: Resolvable path designs
cites work: Handcuffed designs
cites work: Decomposition of a complete multigraph into simple paths: nonbalanced handcuffed designs
full work available at URL: s0195-6698(13)80120-5
OpenAlex ID: W2045675394
description: scientific article; zbMATH DE number 4170950