The longest path in a random graph

Combinatorica volume 1, pages1–12(1981)Cite this article

Abstract

A random graph with (1+ε)n/2 edges contains a path of lengthcn. A random directed graph with (1+ε)n edges contains a directed path of lengthcn. This settles a conjecture of Erdõs.

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References

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    P. Erdős andA. Rényi, On the evolution of random graphs,Publications of the Math. Inst. the Hung. Acad. of Sci.,5 (1960), 17–61.

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    W. F. de la Vega, Sur la plus grande longueur des chemins élémentaires de graphes aléatoires,Preprint of Laboratoire d’informatique pour les Sciences de l’Homme, C.N.R.S., 1979.

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    P. Erdős, Problems and results on finite and infinite graphs, inProc. Symp. Prague 1974, Akademia Praha 1975.

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Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, H-1053, Budapest, Hungary

    Miklós Ajtai, János Komlós & Endre Szemerédi

Authors
  1. Miklós Ajtai
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  2. János Komlós
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  3. Endre Szemerédi
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Ajtai, M., Komlós, J. & Szemerédi, E. The longest path in a random graph. Combinatorica 1, 1–12 (1981). https://doi.org/10.1007/BF02579172

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AMS subject classification (1980)

  • 05 C 38
  • 60 C 05
  • 60 J 80