|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Random graphs from a minor-closed class
If you have a question about this talk, please contact Andrew Thomason.
There has been much recent interest in random graphs sampled uniformly 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 then use combinatorial and probabilistic methods to extend these results. We will consider random graphs from a `well-behaved’ class of graphs: examples of such classes include all minor-closed classes of graphs with 2-connected excluded minors (such as forests, series-parallel graphs and planar 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 give weights to edges and components to specify probabilities, so that our random graphs correspond to the “random cluster” model, appropriately conditioned. We find that earlier results extend naturally in both directions, to general well-behaved classes of graphs, and to the weighted framework, for example results concerning the probability of a random graph being connected, and we also find new results on the 2-core.
This talk is part of the Combinatorics Seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsCambridge Science Festival Visual rhetoric and modern South Asian history Social Anthropology
Other talksDates, Rates, Ages and Stages: New developments in determining metamorphic timescales Transitive leap frogging: how to avoid queuing up for work The Khmer Rouge Tribunal, ‘civil parties’ and the Cambodian diaspora TBC From proteins to plants: Using algorithmic information theory to study biological evolution and development tba