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CATEGORIES:Combinatorics Seminar
SUMMARY:Random graphs from a minor-closed class - Colin Mc
Diarmid (University of Oxford)
DTSTART;TZID=Europe/London:20121115T143000
DTEND;TZID=Europe/London:20121115T153000
UID:TALK40745AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/40745
DESCRIPTION:There has been much recent interest in random grap
hs sampled uniformly from the n-vertex graphs in a
suitable minor-closed class\, such as the class o
f all planar graphs. We shall recall some backgrou
nd\, and then use combinatorial and probabilistic
methods to extend these results.\nWe will consider
random graphs from a `well-behaved' class of grap
hs: examples of such classes include all minor-clo
sed classes of graphs with 2-connected excluded mi
nors (such as forests\, series-parallel graphs and
planar graphs)\, the class of graphs embeddable o
n any given surface\, and the class of graphs with
at most k vertex-disjoint cycles. Also\, we will
give weights to edges and components to specify p
robabilities\, so that our random graphs correspon
d to the "random cluster" model\, appropriately co
nditioned.\nWe find that earlier results extend na
turally in both directions\, to general well-behav
ed classes of graphs\, and to the weighted framewo
rk\, for example results concerning the probabilit
y of a random graph being connected\, and we also
find new results on the 2-core.\n
LOCATION:MR12
CONTACT:Andrew Thomason
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