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SUMMARY:Random graphs from a minor-closed class - Colin McDiarmid (Univers
 ity of Oxford)
DTSTART:20121115T143000Z
DTEND:20121115T153000Z
UID:TALK40745@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:There has been much recent interest in random graphs sampled u
 niformly from the n-vertex graphs in a suitable minor-closed class\, such 
 as the class of all planar graphs. We shall recall some background\, and t
 hen use combinatorial and probabilistic methods to extend these results.\n
 We will consider random graphs from a `well-behaved' class of graphs: exam
 ples of such classes include all minor-closed classes of graphs with 2-con
 nected excluded minors (such as forests\, series-parallel graphs and plana
 r graphs)\, the class of graphs embeddable on any given surface\, and the 
 class of graphs with at most k vertex-disjoint cycles.  Also\, we will giv
 e weights to edges and components to specify probabilities\, so that our r
 andom graphs correspond to the "random cluster" model\, appropriately cond
 itioned.\nWe find that earlier results extend naturally in both directions
 \, to general well-behaved classes of graphs\, and to the weighted framewo
 rk\, for example results concerning the probability of a random graph bein
 g connected\, and we also find new results on the 2-core.\n
LOCATION:MR12
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