Israel Journal of Mathematics

, Volume 1, Issue 3, pp 156–160

On the structure of linear graphs

  • P. Erdös


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Turán, P., 1941,Mat. Lapok,48, 436–452 (Hungarian), see also Turan, P., 1955, On the theory of graphs,Coll. Math.,3, 19–30.MATHGoogle Scholar
  2. 2.
    Dirac, G., will appear inActa Math. Acad. Sci. Hungar Google Scholar
  3. 3.
    Erdös, P., 1947, Some remarks on the theory of graphs,Bull. Amer, Math. Soc.,53, 292–294; see also Erdös, P. and Renyi, A., 1960, On the evolution of random graphs,Publ. Math. Inst. Hung. Acad,5, 17–61.MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Erdös, P. and Stone, A. H., 1946, On the structure of linear graphs,Bull. Amer. Math. Soc.,52, 1087–1091.MATHMathSciNetGoogle Scholar
  5. 5.
    Erdös, P., 1938, On sequences of integers no one of which divides the product of two others and on some related problems,Izv. Nauk. Inst. Mat. Mech. Tomsk.,2, 74–82.Google Scholar
  6. 6.
    Erdös, P., 1962, On the theorem of Rademacher-Turán,Illinois J. of Math.,6, 122–127.MATHGoogle Scholar
  7. 7.
    Erdös, P. and Gallai, T., 1959, On maximal paths and circuits of graphs,Acta. Math. Acad. Sci. Hungar.,10, 337–356.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1963

Authors and Affiliations

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

Personalised recommendations