Random planar graphs with bounds on the maximum and minimum degrees

Details Random planar graphs with bounds on the maximum and minimum degrees Random planar graphs with bounds on the maximum and minimum degrees

2011-01-27

arxiv.org/abs/1101.5288v1

Graphs and Combinatorics (2011)27:87-107

Mathematics

Combinatorics

24 pages, 12 figures

Scientific paper

10.1007/s00373-010-0960-7

Let P_{n,d,D} denote the graph taken uniformly at random from the set of all
labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and
maximum degree at most D(n). We use counting arguments to investigate the
probability that P_{n,d,D} wll contain given components and subgraphs, showing
exactly when this is bounded away from 0 and 1 as n tends to infinity.

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