Clique coverings of the edges of a random graph

Abstract

The edges of the random graph (with the edge probabilityp=1/2) can be covered usingO(n 2lnlnn/(lnn)2) cliques. Hence this is an upper bound on the intersection number (also called clique cover number) of the random graph. A lower bound, obtained by counting arguments, is (1−ɛ)n 2/(2lgn)2.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    B. Bollobás: The chromatic number of the random graph,Combinatorica 8 (1988).

  2. [2]

    P. Erdős, A. Goodman, andL. Pósa: The representation of a graph by set intersections.Canad. J. Math. 18 (1966), 106–112.

    Google Scholar 

  3. [3]

    P. Erdős andD.B. West: A note on the interval number of a graph.Disc. Math. 55 (1985), 129–133.

    Google Scholar 

  4. [4]

    J.R. Griggs: Extremal values of the interval number of a graph, II.Disc. Math. 28 (1979), 37–47.

    Google Scholar 

  5. [5]

    J.R. Griggs andD.B. West: Extremal values of the interval number of a graph, I.SIAM J. Alg. Disc. Meth. 1 (1980), 1–7.

    Google Scholar 

  6. [6]

    D.W. Matula: The largest clique size in a random graph, Tech. Rep. Dept. Comp. Sci. Southern Methodist Univ., Dallas [1976].

    Google Scholar 

  7. [7]

    E.R. Scheinerman On the interval number of random graphs,Discrete Math. 82 (1990), 105–109.

    Google Scholar 

  8. [8]

    J. Spinrad, G. Vijayan, andD.B. West: An improved edge bound on the interval number of a graph.J. Graph Th. 11 (1987), 447–449.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

Research supported in part by ONR Grant N00014-85K0570 and by NSA/MSP Grant MDA904-90-H-4011.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bollobás, B., Erdős, P., Spencer, J. et al. Clique coverings of the edges of a random graph. Combinatorica 13, 1–5 (1993). https://doi.org/10.1007/BF01202786

Download citation

AMS subject classification code (1991)

  • 05 C 80