## Abstract An (__n, q__) graph has __n__ labeled points, __q__ edges, and no loops or multiple edges. The number of connected (__n, q__) graphs is __f(n, q)__. Cayley proved that __f(n, n__^‐1^) = __n__^n−2^ and Renyi found a formula for __f(n, n)__. Here I develop two methods to calculate the exp
The number of connected sparsely edged uniform hypergraphs
✍ Scribed by Michakl Karoński; Tomasz kLuczak
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 684 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
Certain families of d-uniform hypergraphs are counted. In particular, the number of connected d-uniform hypergraphs with r vertices and r + k hyperedges, where k = o(log r/log tog r), is found.
📜 SIMILAR VOLUMES
## Abstract The number of connected graphs on __n__ labeled points and __q__ lines (no loops, no multiple lines) is __f(n,q).__ In the first paper of this series I showed how to find an (increasingly complicated) exact formula for __f(n,n+k)__ for general __n__ and successive __k.__ The method woul
## Abstract We have written computer programs to determine exactly the coefficients in Wright's formula for __f(n, n + k)__, the number of connected sparsely edged labeled graphs (see preceding paper), and used them up to __k__ = 24. We give the results up to __k__ = 7.
The number of nonseparable graphs on n labeled points and q lines is u(n, 9). In the second paper of this series an exact formula for u(n, n + k) was found for general n and successive (small) k. The method would give an asymptotic approximation for fixed k as n + 30. Here an asymptotic approximatio
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