ArticleOriginal scientific text

Title

In-degree sequence in a general model of a random digraph

Authors 1, 1

Affiliations

  1. Department of Algorithmics and Programming, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

Abstract

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.

Keywords

degree sequence, general model of a random digraph

Bibliography

  1. B. Bollobás, Degree sequences of random graphs, Discrete Math. 33 (1981) 1-19, doi: 10.1016/0012-365X(81)90253-3.
  2. B. Bollobás, Vertices of given degree in a random graph, J. Graph Theory 6 (1982) 147-155, doi: 10.1002/jgt.3190060209.
  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.
  4. W. Feller, An introduction to Probability and Its Applications, Vol. 1, 2nd ed. (John Wiley, 1957).
  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.
  6. J. Jaworski and I. Smit, On a random digraph, Annals of Discrete Math. 33 (1987) 111-127.
  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.
  8. J. Jaworski and Z. Palka, Remarks on a general model of a random digraph, Ars Combin. 65 (2002) 135-144.
  9. Z. Palka, Extreme degrees in random graphs, J. Graph Theory 11 (1987) 121-134, doi: 10.1002/jgt.3190110202.
  10. Z. Palka, Rulers and slaves in a random graph, Graphs and Combinatorics 2 (1986) 165-172, doi: 10.1007/BF01788089.
  11. Z. Palka, Asymptotic properties of random graphs, Dissertationes Math. (Rozprawy Mat.) 275 (1988).
  12. Z. Palka, Some remarks about extreme degrees in a random graph, Math. Proc. Camb. Philos. Soc. 3 (1994) 13-26.
Pages:
193-207
Main language of publication
English
Received
2004-09-09
Accepted
2006-01-12
Published
2006
Exact and natural sciences