期刊
JOURNAL OF COMBINATORIAL THEORY SERIES B
卷 93, 期 2, 页码 187-205出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jctb.2004.09.007
关键词
random; labelled; planar; graph; counting
类别
We study various properties of the random planar graph R-n drawn uniformly at random from the class P-n of all simple planar graphs on n labelled vertices. In particular, we show that the probability that R-n is connected is bounded away from 0 and from 1. We also show for example that each positive integer k, with high probability R-n has linearly many vertices of a given degree, in each embedding R-n has linearly many faces of a given size, and R-n has exponentially many automorphisms. (C) 2004 Elsevier Inc. All rights reserved.
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