A distributive lattice on the set of perfect matchings of a plane bipartite graph
type: Item
instance of: scholarly article
title: A distributive lattice on the set of perfect matchings of a plane bipartite graph
zbMATH Open document ID: 1025.05050
DOI: 10.1023/A:1024483217354
author: P. C. B. Lam
author: Heping Zhang
published in: Order
publication date: 2003-08-21T00:00:00Z
review text: Perfect matchings of (finite simple) graphs \(G\) have been widely studied over a (relatively) long time and the literature on this subject is considerable. Even so, interesting additions continue to be made as is quite clear from this paper where \(M(G)\), the set of perfect matchings, is provided a graph structure (edge means matchings differ by only one cycle that is the boundary of an inner face of \(G\)) whose acyclic orientation turns \(M(G)\) into a poset whose Hasse diagram is isomorphic to the \(Z\)-transformation graph and which is a distributive lattice via the elegant proof of the main theorem involving an embedding result employing certain combinatorial functions on the set of inner faces of \(G\), producing an important observation as a result.
reviewed by: J. Neggers
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 92E10
Mathematics Subject Classification ID: 05C90
Mathematics Subject Classification ID: 06D99
zbMATH DE Number: 1968899
zbMATH Keywords: distributive lattice
zbMATH Keywords: poset
zbMATH Keywords: perfect matching
zbMATH Keywords: Z-transformation graph
zbMATH Keywords: plane bipartite graph
MaRDI profile type: Publication
full work available at URL: a:1024483217354
OpenAlex ID: W26303559
description: scientific article; zbMATH DE number 1968899