Paper Info
Title
Bridge-Addability, Edge-Expansion and Connectivity.
Abstract
alpha A class of graphs is called bridge-addable if, for each graph in the class and each pair u and v of vertices in different components, the graph obtained by adding an edge joining u and v must also be in the class. The concept was introduced in 2005 by McDiarmid, Steger and Welsh, who showed that, for a random graph sampled uniformly from such a class, the probability that it is connected is at least 1/e. We generalize this and related results to bridge-addable classes with edge-weights which have an edge-expansion property. Here, a graph is sampled with probability proportional to the product of its edge-weights. We obtain for example lower bounds for the probability of connectedness of a graph sampled uniformly from a relatively bridge-addable class of graphs, where some but not necessarily all of the possible bridges are allowed to be introduced. Furthermore, we investigate whether these bounds are tight, and in particular give detailed results about random forests in complete balanced multipartite graphs.
Year
DOI
Venue
2017
10.1017/S0963548317000128
COMBINATORICS PROBABILITY & COMPUTING
Field
DocType
Volume
Discrete mathematics,Mathematics
Journal
26
Issue
ISSN
Citations 
5
0963-5483
0
PageRank 
References 
Authors
0.34
5
2
Name
Order
Citations
PageRank
Colin McDiarmid11071167.05
Kerstin Weller200.68