Enumeration and limit laws for series-parallel graphs
نویسندگان
چکیده
We show that the number gn of labelled series–parallel graphs on n vertices is asymptotically gn ∼ g · n−5/2γ nn!, where γ and g are explicit computable constants. We show that the number of edges in random series–parallel graphs is asymptotically normal with linear mean and variance, and that it is sharply concentrated around its expected value. Similar results are proved for labelled outerplanar graphs and for graphs not containing K2,3 as a minor. c © 2007 Elsevier Ltd. All rights reserved.
منابع مشابه
Enumeration and Limit Laws of Series-parallel Graphs
We show that the number gn of labelled series-parallel graphs on n vertices is asymptotically gn ∼ g · n−5/2γnn!, where γ and g are explicit computable constants. We show that the number of edges in random seriesparallel graphs is asymptotically normal with linear mean and variance, and that it is sharply concentrated around its expected value. Similar results are proved for labelled outerplana...
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عنوان ژورنال:
- Eur. J. Comb.
دوره 28 شماره
صفحات -
تاریخ انتشار 2007