A general model of a random digraph D(n,P) is considered. Based on a precise estimate of the asymptotic behaviour of the distribution function of the binomial law, a problem of the distribution of extreme in-degrees of D(n,P) is discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1312, author = {Zbigniew Palka and Monika Sperling}, title = {In-degree sequence in a general model of a random digraph}, journal = {Discussiones Mathematicae Graph Theory}, volume = {26}, year = {2006}, pages = {193-207}, zbl = {1142.05073}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1312} }
Zbigniew Palka; Monika Sperling. In-degree sequence in a general model of a random digraph. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 193-207. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1312/
[000] [1] B. Bollobás, Degree sequences of random graphs, Discrete Math. 33 (1981) 1-19, doi: 10.1016/0012-365X(81)90253-3. | Zbl 0447.05038
[001] [2] B. Bollobás, Vertices of given degree in a random graph, J. Graph Theory 6 (1982) 147-155, doi: 10.1002/jgt.3190060209. | Zbl 0499.05056
[002] [3] P. Erdős and A. Rényi, On the strength of connectedness of a random graph, Acta Math. Acad. Sci. Hung. 12 (1961) 261-267, doi: 10.1007/BF02066689. | Zbl 0103.16302
[003] [4] W. Feller, An introduction to Probability and Its Applications, Vol. 1, 2nd ed. (John Wiley, 1957). | Zbl 0077.12201
[004] [5] G. Ivchenko, On the asymptotic behaviour of degrees of vertices in a random graph, Theory Probab. Appl. 18 (1973) 188-196, doi: 10.1137/1118020.
[005] [6] J. Jaworski and I. Smit, On a random digraph, Annals of Discrete Math. 33 (1987) 111-127. | Zbl 0633.05030
[006] [7] J. Jaworski and M. Karoński, On the connectivity of graphs generated by a sum of random mappings, J. Graph Theory 17 (1993) 135-150, doi: 10.1002/jgt.3190170203. | Zbl 0782.05073
[007] [8] J. Jaworski and Z. Palka, Remarks on a general model of a random digraph, Ars Combin. 65 (2002) 135-144. | Zbl 1071.05574
[008] [9] Z. Palka, Extreme degrees in random graphs, J. Graph Theory 11 (1987) 121-134, doi: 10.1002/jgt.3190110202. | Zbl 0672.05069
[009] [10] Z. Palka, Rulers and slaves in a random graph, Graphs and Combinatorics 2 (1986) 165-172, doi: 10.1007/BF01788089. | Zbl 0606.92028
[010] [11] Z. Palka, Asymptotic properties of random graphs, Dissertationes Math. (Rozprawy Mat.) 275 (1988). | Zbl 0675.05055
[011] [12] Z. Palka, Some remarks about extreme degrees in a random graph, Math. Proc. Camb. Philos. Soc. 3 (1994) 13-26.