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The structure and distances in Yule recursive trees
Article first published online: 19 JUL 2007
DOI: 10.1002/rsa.20183
Copyright © 2007 Wiley Periodicals, Inc.
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Additional Information
How to Cite
Feng, Q. and Su, C. (2007), The structure and distances in Yule recursive trees. Random Structures & Algorithms, 31: 273–287. doi: 10.1002/rsa.20183
Publication History
- Issue published online: 29 AUG 2007
- Article first published online: 19 JUL 2007
- Manuscript Accepted: 5 APR 2007
- Manuscript Revised: 7 DEC 2006
- Manuscript Received: 28 MAR 2005
Funded by
- National Natural Science Foundation. Grant Number: 10671188
- Knowledge Innovation Program of CAS. Grant Number: KJCX3-SYW-S02
- USTC
- Abstract
- References
- Cited By
Keywords:
- uniform recursive trees;
- Yule recursive trees;
- isomorphism;
- branch;
- distance
Abstract
Based on uniform recursive trees, we introduce random trees with the factor of time, which are named Yule recursive trees. The structure and the distance between the vertices in Yule recursive trees are investigated in this paper. For arbitrary time t > 0, we first give the probability that a Yule recursive tree Yt is isomorphic to a given rooted tree γ; and then prove that the asymptotic distribution of ζt,m, the number of the branches of size m, is the Poisson distribution with parameter λ = 1/m. Finally, two types of distance between vertices in Yule recursive trees are studied, and some limit theorems for them are established.© 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007