Clique covering of graphs

Abstract

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.

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References

  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 

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Pyber, L. Clique covering of graphs. Combinatorica 6, 393–398 (1986). https://doi.org/10.1007/BF02579265

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AMS subject classification (1980)

  • 05 C 35