Combinatorica

, Volume 22, Issue 2, pp 269–274 | Cite as

Large Cliques in \(\)-Free Graphs

  • András Gyárfás
  • Alice Hubenko
  • József Solymosi
Original Paper

Dedicated to the memory of Paul Erdős

A graph is called \(\)-free if it contains no cycle of length four as an induced subgraph. We prove that if a \(\)-free graph has n vertices and at least \(\) edges then it has a complete subgraph of \(\) vertices, where \(\) depends only on \(\). We also give estimates on \(\) and show that a similar result does not hold for H-free graphs––unless H is an induced subgraph of \(\). The best value of \(\) is determined for chordal graphs.

AMS Subject Classification (2000) Classes:  05C35 

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Copyright information

© János Bolyai Mathematical Society, 2002

Authors and Affiliations

  • András Gyárfás
    • 1
  • Alice Hubenko
    • 2
  • József Solymosi
    • 3
  1. 1.Computer and Automation Research Institute, Hungarian Academy of Sciences; E-mail: Gyarfas@luna.aszi.sztaki.huHU
  2. 2.Computer and Automation Research Institute, Hungarian Academy of Sciences; E-mail: hubenko@msci.memphis.eduHU
  3. 3.Computer and Automation Research Institute, Hungarian Academy of Sciences; E-mail: solymosi@euclid.ucsd.eduHU

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