Clique covering of graphs


Let cc(G) denote the least number of complete subgraphs necessary to cover the edges of a graphG. Erdős conjectured that for a graphG onn vertices

$$cc(G) + cc(\bar G) \leqq \frac{1}{4}n^2 + 2$$

ifn is sufficiently large. We prove this conjecture.

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


  1. [1]

    D. de Caen, P. Erdős, N. J. Pullman andN. C. Wormald, Extremal Clique Coverings of Complementary Graphs,Combinatorica 6 (1986), 309–314.

    MATH  MathSciNet  Google Scholar 

  2. [2]

    P. Erdős, On a theorem of Rademacher—Turán,Illinois J. of Maths. 6 (1962), 122–127.

    Google Scholar 

  3. [3]

    P. Erdős, A. W. Goodman andL. Pósa, The Representation of a Graph by Set Intersections,Can. J. Math. 18 (1966), 106–112.

    Google Scholar 

  4. [4]

    P. Erdős andG. Szekeres, A combinatorial problem in geometry,Compositio Math. 2 (1935), 464–470.

    Google Scholar 

  5. [5]

    D. Taylor, R. D. Dutton andR. C. Brigham, Bounds on Nordhaus — Gaddum Type Bounds for Clique Cover Numbers,Congressus Num. 40 (1983), 388–398.

    MathSciNet  Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pyber, L. Clique covering of graphs. Combinatorica 6, 393–398 (1986).

Download citation

AMS subject classification (1980)

  • 05 C 35