Paper Info
Title
Random Graphs from a Weighted Minor-Closed Class.
Abstract
There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a more general model. We consider random graphs from a 'well-behaved' class of graphs: examples of such classes include all minor-closed classes of graphs with 2-connected excluded minors (such as forests, series-parallel graphs and planar graphs), the class of graphs embeddable on any given surface, and the class of graphs with at most k vertex-disjoint cycles. Also, we give weights to edges and components to specify probabilities, so that our random graphs correspond to the random cluster model, appropriately conditioned. We find that earlier results extend naturally in both directions, to general well-behaved classes of graphs, and to the weighted framework, for example results concerning the probability of a random graph being connected; and we also give results on the 2-core which are new even for the uniform (unweighted) case.
Year
Venue
Keywords
2013
ELECTRONIC JOURNAL OF COMBINATORICS
random graph,minor-closed class,random cluster model,connectivity,core
Field
DocType
Volume
Discrete mathematics,Modular decomposition,Indifference graph,Combinatorics,Random graph,Chordal graph,Clique-sum,Pathwidth,Mathematics,Trapezoid graph,Maximal independent set
Journal
20
Issue
ISSN
Citations 
2.0
1077-8926
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Colin McDiarmid11071167.05