Random free trees and forests with constraints on multiplicities of vertices
β Scribed by Timashov, A. N.
- Book ID
- 120137526
- Publisher
- Walter de Gruyter GmbH & Co. KG
- Year
- 2004
- Tongue
- English
- Weight
- 101 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0924-9265
No coin nor oath required. For personal study only.
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If a graph G with cycle rank p contains both spanning trees with rn and with n end-vertices, rn < n, then G has at least 2p spanning trees with k end-vertices for each integer k, rn < k < n. Moreover, the lower bound of 2p is best possible. [ l ] and Schuster [4] independently proved that such span
A randomly evolving graph, with vertices immigrating at rate n and each possible edge appearing at rate 1/n, is studied. The detailed picture of emergence of giant components with O n 2/3 vertices is shown to be the same as in the ErdΕs-RΓ©nyi graph process with the number of vertices fixed at n at t