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A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs
Open accessAbstract
Let Δ and n be natural numbers such that Δn = 2m is even and Δ ⩽ (2 log n )1/2 - 1. Then as n →, the number of labelled Δ-regular graphs on n vertices is asymptotic to e − λ − λ 2 ( 2 m ) ! m ! 2 m ( Δ ! ) m where λ = (Δ -1)/2. As a consequence of the method we determine the asymptotic distribution of the number of short cycles in graphs with a given degree sequence, and give analogous formulae for hypergraphs.
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Metadata
- Authors
- Bollobás, B.
- Venue
- European Journal of Combinatorics
- Publisher
- Elsevier BV
- Published
- 1980-12
- Volume
- 1
- Issue
- 4
- Pages
- 311-316
- ISSN
- 0195-6698 (ISSN-L)
- OpenAlex
- W2091476183
- Cited by
- 1,151
- References
- 0
- FWCI
- 4.50
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Bollobás, B. (1980). A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs. European Journal of Combinatorics. https://doi.org/10.1016/s0195-6698(80)80030-8
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