Poisson convergence of numbers of vertices of a given degree in random graphs

Wojciech Kordecki

Discussiones Mathematicae Graph Theory (1996)

• Volume: 16, Issue: 2, page 157-172
• ISSN: 2083-5892

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Abstract

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The asymptotic distributions of the number of vertices of a given degree in random graphs, where the probabilities of edges may not be the same, are given. Using the method of Poisson convergence, distributions in a general and particular cases (complete, almost regular and bipartite graphs) are obtained.

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Wojciech Kordecki. "Poisson convergence of numbers of vertices of a given degree in random graphs." Discussiones Mathematicae Graph Theory 16.2 (1996): 157-172. <http://eudml.org/doc/270487>.

@article{WojciechKordecki1996,
abstract = {The asymptotic distributions of the number of vertices of a given degree in random graphs, where the probabilities of edges may not be the same, are given. Using the method of Poisson convergence, distributions in a general and particular cases (complete, almost regular and bipartite graphs) are obtained.},
author = {Wojciech Kordecki},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Random graphs; degrees of vertices; Poisson convergence; random graphs},
language = {eng},
number = {2},
pages = {157-172},
title = {Poisson convergence of numbers of vertices of a given degree in random graphs},
url = {http://eudml.org/doc/270487},
volume = {16},
year = {1996},
}

TY - JOUR
AU - Wojciech Kordecki
TI - Poisson convergence of numbers of vertices of a given degree in random graphs
JO - Discussiones Mathematicae Graph Theory
PY - 1996
VL - 16
IS - 2
SP - 157
EP - 172
AB - The asymptotic distributions of the number of vertices of a given degree in random graphs, where the probabilities of edges may not be the same, are given. Using the method of Poisson convergence, distributions in a general and particular cases (complete, almost regular and bipartite graphs) are obtained.
LA - eng
KW - Random graphs; degrees of vertices; Poisson convergence; random graphs
UR - http://eudml.org/doc/270487
ER -

References

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1. [1] A.D. Barbour, Poisson convergence and random graphs, Math. Proc. Camb. Phil. Soc. 92 (1982) 349-359, doi: 10.1017/S0305004100059995. Zbl0498.60016
2. [2] A.D. Barbour and G.K. Eagleason, Poisson approximation for some statistics based on exchangeable trials, Adv. Appl. Prob. 15 (1983) 585-600, doi: 10.2307/1426620. Zbl0511.60025
3. [3] A.D. Barbour, L. Holst and S. Janson, Poisson approximation (Clarendon Press, Oxford, 1992). Zbl0746.60002
4. [4] M. Karoński and A. Ruciński, Poisson convergence and semiinduced properties of random graphs, Math. Proc. Camb. Phil. Soc. 101 (1987) 291-300, doi: 10.1017/S0305004100066664. Zbl0627.60016
5. [5] V.L. Klee, D.G. Larman and E.M. Wright, The proportion of labelled bipartite graphs which are connected, J. London Math. Soc. 24 (1981) 397-404, doi: 10.1112/jlms/s2-24.3.397. Zbl0452.05040
6. [6] W. Kordecki, Vertices of given degree in a random graph, Prob. Math. Stat. 11 (1991) 287-290. Zbl0753.60015
7. [7] Z. Palka, On the degrees of vertices in a bichromatic random graph, Period. Math. Hung. 15 (1984) 121-126, doi: 10.1007/BF01850725. Zbl0514.05053
8. [8] Z. Palka, Asymptotic properties of random graphs, Dissertationes Mathematicae, CCLXXV (PWN, Warszawa, 1998). Zbl0675.05055
9. [9] Z. Palka and A. Ruciński, Vertex-degrees in a random subgraph of a regular graph, Studia Scienc. Math. Hung. 25 (1990) 209-214. Zbl0643.60009

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