Advertisement
Published in:
2006 | OriginalPaper | Chapter
Random Graphs from Planar and Other Addable Classes
Authors : Colin McDiarmid, Angelika Steger, Dominic J. A. Welsh
Published in: Topics in Discrete Mathematics
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
We study various properties of a random graph
R
n
, drawn uniformly at random from the class
$$ \mathcal{A}_n $$
of all simple graphs on
n
labelled vertices that satisfy some given property, such as being planar or having tree-width at most κ. In particular, we show that if the class
$$ \mathcal{A} $$
is’ small’ and ‘addable’, then the probability that
R
n
is connected is bounded away from 0 and from 1. As well as connectivity we study the appearances of subgraphs, and thus also vertex degrees and the numbers of automorphisms. We see further that if
$$ \mathcal{A} $$
is’ smooth’ then we can make much more precise statements for example concerning connectivity.