Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T14:37:18.439Z Has data issue: false hasContentIssue false
  • English
  • Français

On colouring random graphs

Published online by Cambridge University Press:  24 October 2008

G. R. Grimmett  and
C. J. H. McDiarmid
G. R. Grimmett
Affiliation:
Mathematical Institute, Oxford
C. J. H. McDiarmid
Affiliation:
Mathematical Institute, Oxford
Get access Rights & Permissions [Opens in a new window]

Abstract

Let ωn denote a random graph with vertex set {1, 2, …, n}, such that each edge is present with a prescribed probability p, independently of the presence or absence of any other edges. We show that the number of vertices in the largest complete subgraph of ωn is, with probability one,

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 2 , March 1975 , pp. 313 - 324
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Erdös, P. and Rényi, A.On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5A (1960), 17–61.Google Scholar
(2)Harary, F.Graph theory (1969) Addison–Wesley.CrossRefGoogle Scholar
(3)Holgate, P.Majorants of the chromatic number of a random graph. J. Roy. Statist. Soc. Ser. B 31 (1969), 303–309.Google Scholar
(4)Matula, D. W.On the complete subgraphs of a random graph. Proc. 2nd. Conf. Comb. Th. and Appl. (1970) Chapel Hill, 356–369.Google Scholar
(5)Matula, D. W., Marble, G. and Isaacson, J. D. Graph colouring algorithms, in Graph theory and computing (1972) Academic Press, London, 109–122.Google Scholar
(6)Welsh, D. J. A. and Powell, M. B.An upper bound for the chromatic number of a graph and its application to timetabling problems. Comput. J. 10 (1967), 85–86.CrossRefGoogle Scholar
(7)Wilf, H. S.The eigenvalues of a graph and its chromatic number. J. London Math. Soc. 42 (1967), 330–332.CrossRefGoogle Scholar
(8)Wilson, R. J.Introduction to graph theory (1972) Oliver and Boyd, Edinburgh.Google Scholar
(9)Grimmett, G. R.Random Graph Theorems. Proc. 7th Prague Conf. on Information Theory and related topics (1974), in press.Google Scholar