Abstract
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, log in via an institution to check access.
Similar content being viewed by others
References
J. A. Bondy andU. S. R. Murty,Graph theory with applications, Problem 6.
A. Donald, An upper bound for the path number of a graph,Journal of Graph Theory,4 (1980), 189–201
P. Erdős, A. W. Goodman andL. Pósa, The representation of a graph by set intersections,Canad. J. Math.,18 (1966), 106–112.
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.
L. Lovász, A brief survey of matroid theory,Matematikai Lapok,22 (1971), 249–267.
L. Lovász,Combinatorial problems and exercises, North-Holland, 1979, 266–267, 332.
C. St. J. A. Nash-Williams, An application of matroids to graph theory,I. C. C. Rome/Dunod—Gordon and Breach, 1967, 263–265.
Tao Mao-qi, Shen Yun-qiu andKu Tung-hsin, An Erdős conjecture—The planar case,preprint.
D. J. A. Welsh,Matroid theory, Academic Press, London, New York, San Francisco, 1976.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pyber, L. An erdős—Gallai conjecture. Combinatorica 5, 67–79 (1985). https://doi.org/10.1007/BF02579444
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02579444