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

Discussiones Mathematicae Graph Theory (1996)

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

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topWojciech 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

top- [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] 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] A.D. Barbour, L. Holst and S. Janson, Poisson approximation (Clarendon Press, Oxford, 1992). Zbl0746.60002
- [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] 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] W. Kordecki, Vertices of given degree in a random graph, Prob. Math. Stat. 11 (1991) 287-290. Zbl0753.60015
- [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] Z. Palka, Asymptotic properties of random graphs, Dissertationes Mathematicae, CCLXXV (PWN, Warszawa, 1998). Zbl0675.05055
- [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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