Poisson convergence of numbers of vertices of a given degree in random graphs
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 157-172.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: Random graphs, degrees of vertices, Poisson convergence
@article{DMGT_1996_16_2_a6,
     author = {Kordecki, Wojciech},
     title = {Poisson convergence of numbers of vertices of a given degree in random graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {157--172},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a6/}
}
TY  - JOUR
AU  - Kordecki, Wojciech
TI  - Poisson convergence of numbers of vertices of a given degree in random graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 1996
SP  - 157
EP  - 172
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a6/
LA  - en
ID  - DMGT_1996_16_2_a6
ER  - 
%0 Journal Article
%A Kordecki, Wojciech
%T Poisson convergence of numbers of vertices of a given degree in random graphs
%J Discussiones Mathematicae. Graph Theory
%D 1996
%P 157-172
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a6/
%G en
%F DMGT_1996_16_2_a6
Kordecki, Wojciech. Poisson convergence of numbers of vertices of a given degree in random graphs. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 157-172. http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a6/

[1] A.D. Barbour, Poisson convergence and random graphs, Math. Proc. Camb. Phil. Soc. 92 (1982) 349-359, doi: 10.1017/S0305004100059995.

[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.

[3] A.D. Barbour, L. Holst and S. Janson, Poisson approximation (Clarendon Press, Oxford, 1992).

[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.

[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.

[6] W. Kordecki, Vertices of given degree in a random graph, Prob. Math. Stat. 11 (1991) 287-290.

[7] Z. Palka, On the degrees of vertices in a bichromatic random graph, Period. Math. Hung. 15 (1984) 121-126, doi: 10.1007/BF01850725.

[8] Z. Palka, Asymptotic properties of random graphs, Dissertationes Mathematicae, CCLXXV (PWN, Warszawa, 1998).

[9] Z. Palka and A. Ruciński, Vertex-degrees in a random subgraph of a regular graph, Studia Scienc. Math. Hung. 25 (1990) 209-214.