Random Graphs from Planar and Other Addable Classes [chapter]

Colin McDiarmid, Angelika Steger, Dominic J. A. Welsh
Algorithms and Combinatorics  
We study various properties of a random graph R n , drawn uniformly at random from the class 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 k. In particular, we show that if the class 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
more » ... We see further that if A is 'smooth' then we can make much more precise statements for example concerning connectivity.
doi:10.1007/3-540-33700-8_15 fatcat:7ccpxhzf5vczzpzdyg4fa3sgsu