An erdős—Gallai conjecture


The following conjecture of P. Erdős and T. Gallai is confirmed: every graph onn vertices can be covered byn−1 circuits and edges.

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


  1. [1]

    J. A. Bondy andU. S. R. Murty,Graph theory with applications, Problem 6.

  2. [2]

    A. Donald, An upper bound for the path number of a graph,Journal of Graph Theory,4 (1980), 189–201

    MATH  MathSciNet  Google Scholar 

  3. [3]

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

    MathSciNet  Google Scholar 

  4. [4]

    L. Lovász, On covering of graphs, in:Theory of graphs, Proceedings of the Colloquium held at Tihany, Hungary, 1966, (ed: P. Erdős and G.O.H. Katona), Academic Press, New York, 1968, 231–236.

    Google Scholar 

  5. [5]

    L. Lovász, A brief survey of matroid theory,Matematikai Lapok,22 (1971), 249–267.

    MathSciNet  Google Scholar 

  6. [6]

    L. Lovász,Combinatorial problems and exercises, North-Holland, 1979, 266–267, 332.

  7. [7]

    C. St. J. A. Nash-Williams, An application of matroids to graph theory,I. C. C. Rome/Dunod—Gordon and Breach, 1967, 263–265.

  8. [8]

    Tao Mao-qi, Shen Yun-qiu andKu Tung-hsin, An Erdős conjecture—The planar case,preprint.

  9. [9]

    D. J. A. Welsh,Matroid theory, Academic Press, London, New York, San Francisco, 1976.

    Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pyber, L. An erdős—Gallai conjecture. Combinatorica 5, 67–79 (1985).

Download citation

AMS subject classification (1980)

  • 05 C 38