AG 1   Info

AG Audience

English

30 Minutes

Saarbrücken

We will study how typical specimen of various classes of planar maps (i.e., embedded planar graphs) look like. In particular, we are interested in the degree sequence of a random map drawn from all maps of equal size. For ordinary random maps, it is known that the expected number of vertices of a fixed degree is linear in the number of edges of that map. Moreover, this number is sharply concentrated around its expectation for which an asymptotic formula (depending on the given degree) exists. We will see how this result can be transfered to other classes of random maps like those that are biconnected, 3-connected, loopless, bridgeless, or simple.

This is joint work with Konstantinos Panagiotou.

Daniel Johannsen

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