Israel Journal of Mathematics

, Volume 1, Issue 3, pp 156–160

On the structure of linear graphs

  • P. Erdös

DOI: 10.1007/BF02759702

Cite this article as:
Erdös, P. Israel J. Math. (1963) 1: 156. doi:10.1007/BF02759702


Denote byG(n; m) a graph ofn vertices andm edges. We prove that everyG(n; [n2/4]+1) contains a circuit ofl edges for every 3 ≦l<c2n, also that everyG(n; [n2/4]+1) contains ake(un, un) withun=[c1 logn] (for the definition ofke(un, un) see the introduction). Finally fort>t0 everyG(n; [tn3/2]) contains a circuit of 2l edges for 2≦l<c3t2.

Copyright information

© Hebrew University 1963

Authors and Affiliations

  • P. Erdös
    • 1
  1. 1.University of MichiganAnn ArborU.S.A.

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