Anzeige
Erschienen in:
2006 | OriginalPaper | Buchkapitel
Random Graphs from Planar and Other Addable Classes
verfasst von : Colin McDiarmid, Angelika Steger, Dominic J. A. Welsh
Erschienen in: Topics in Discrete Mathematics
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. 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.