On the number of perfect matchings and Hamilton cycles in \(\varepsilon\)-regular non-bipartite graphs
type: Item
instance of: scholarly article
title: On the number of perfect matchings and Hamilton cycles in \(\varepsilon\)-regular non-bipartite graphs
zbMATH Open document ID: 0964.05053
published in: The Electronic Journal of Combinatorics
publication date: 2000-11-30T00:00:00Z
full work available at URL: https://eudml.org/doc/121049
full work available at URL: v7i1r57.html
review text: Consider a graph on an even number of vertices \(n\). Let \(m\) denote its number of perfect matchings and \(h\) its number of Hamilton cycles. It is shown that if all local densities deviate at most \(\varepsilon\) from the global density \(d\), then \((h/h!)^{1/n}\) and \(2[(n/2)!m/n!]^{2/n}\) both deviate at most \(2\varepsilon\) from \(d\).
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 1537383
zbMATH Keywords: perfect matchings
zbMATH Keywords: Hamilton cycles
author: Alan Frieze
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1537383