Properties of random difference graphs
type: Item
instance of: scholarly article
title: Properties of random difference graphs
zbMATH Open document ID: 1266.05156
author: Christopher Ross
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v19i4p28
review text: Summary: Generate a bipartite graph on a partitioned set of vertices by randomly assigning to each vertex \(v\) some weight \(w(v) \in [0,1]\) and adding an edge between vertices \(u\) and \(v\) (in distinct parts) if and only if \(w(v) + w(v) > 1\); the results of such processes are known as difference graphs. Random difference graphs of a given size can be produced either by uniformly random generation of weights or by choosing a graph uniformly at random from the set of all such graphs. We prove that these two methods give rise to the same distribution, and use this equivalence to find exact results for the likelihood of connectivity and Hamiltonicity. We also find the distribution of other properties, such as matching number and degeneracy.
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 6171811
zbMATH Keywords: difference graphs
zbMATH Keywords: random graphs
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6171811