Graphs and Combinatorics

, Volume 29, Issue 5, pp 1183–1191 | Cite as

Large Chromatic Number and Ramsey Graphs

  • Csaba BiróEmail author
  • Zoltán Füredi
  • Sogol Jahanbekam
Original Paper


Let Q (n, χ) denote the minimum clique size an n-vertex graph can have if its chromatic number is χ. Using Ramsey graphs we give an exact, albeit implicit, formula for the case χ ≥ (n + 3)/2.


Clique number Chromatic number Ramsey graphs 

Mathematics Subject Classification

05C69 05C35 05D10 


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Copyright information

© Springer 2012

Authors and Affiliations

  • Csaba Biró
    • 1
    Email author
  • Zoltán Füredi
    • 2
    • 3
  • Sogol Jahanbekam
    • 2
  1. 1.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  2. 2.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Rényi Institute of Mathematics of the Hungarian Academy of SciencesBudapestHungary

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