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Random Graphs from Planar and Other Addable Classes
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Algorithms and Combinatorics
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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

doi:10.1007/3-540-33700-8_15
fatcat:7ccpxhzf5vczzpzdyg4fa3sgsu