期刊
COMBINATORICS PROBABILITY & COMPUTING
卷 13, 期 2, 页码 165-183出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0963548303005947
关键词
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We consider random planar graphs on n labelled nodes, and show in particular that if the graph is picked uniformly at random then the expected number of edges is at least 13/7n + o(n). To prove this result we give a lower bound on the size of the set of edges that can be added to a planar graph on n nodes and m edges while keeping it planar, and in particular we see that if m is at most 13/7n - c (for a suitable constant c) then at least this number of edges can be added.
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