Skip to main content
Log in

Small topological complete subgraphs of “dense” graphs

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

A graph ofn vertices and\(4^{t^2 } n^{1 + \varepsilon } \) edges contains aTK t on at most 7t 2 logt/ε vertices. This answers a question of P. Erdős.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. Erdős, On bipartite subgraphs of a graph, (in Hungarian)Matematikai Lapok,18 (1967), 283–288.

    Google Scholar 

  2. P. Erdős, Some Unsolved Problems in Graph Theory and Combinatorial Analysis,Combinatorial Mathematics and its Applications (Proc. Conf. Oxford (1969), 97–109. Academic Press London, 1971.

    Google Scholar 

  3. P. Erdős andT. Gallai, On maximal paths and circuits of graphs,Acta Math. Acad. Sci. Hungar.,10 (1959), 337–356.

    Google Scholar 

  4. W. Mader, Hinreichende Bedingungen für die Existenz von Teilgraphen die zu einem vollständigen Graphen homöomorph sind,Math. Nachr.,53 (1972), 145–150.

    Google Scholar 

  5. N. Sauer, Extremaleigenschaften regularer Graphen gegebener Taillenweite,I. andII.Sitzungberichte Österreich Akad. Wiss. Math. Natur. Kl. S-B II.,176 (1967), 9–25 ibid 176 (1967), 27–43.

    Google Scholar 

  6. W. T. Tutte, A family of cubical graphs,Proc. Cambridge. Philos, Soc.,43 (1947), 459–474.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kostochka, A., Pyber, L. Small topological complete subgraphs of “dense” graphs. Combinatorica 8, 83–86 (1988). https://doi.org/10.1007/BF02122555

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02122555

AMS subject classification (1980)

Navigation