RANDOM PLANAR GRAPHS WITH GIVEN AVERAGE DEGREE
Stefanie Gerke, Colin McDiarmid, Angelika Steger, Andreas Weißl · Oxford University Press eBooks · 2007
This chapter investigates the behaviour of the function γ(q). In particular, it considers γ(q) as q approaches 1 from below and above and 3 from below, and explains the discontinuity as it approach 1 from below by changing scale appropriately. New properties of Rn,q, for example in terms of the number of automorphisms, are investigated. Lower bounds are given on the maximum node degree and the maximum face size of a plane embedding. The relation between the growth constants of labelled and unlabelled planar graphs with given average degree is studied.