Random planar graphs with n nodes and a fixed number of edges.
Let ℘(n, m) be the class of simple labelled planar graphs with n nodes and m edges, and let Rn,q be a graph drawn uniformly at random from ℘(n, ⌊qn⌋). We show properties that hold with high probability (w.h.p.) for Rn,q when 1 < q < 3. For example, we show that Rn,q contains w.h.p. lin...
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SIAM
2005
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