Graphs and Combinatorics

, Volume 29, Issue 5, pp 1183–1191

Large Chromatic Number and Ramsey Graphs

Original Paper

DOI: 10.1007/s00373-012-1179-6

Cite this article as:
Biró, C., Füredi, Z. & Jahanbekam, S. Graphs and Combinatorics (2013) 29: 1183. doi:10.1007/s00373-012-1179-6


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 

Copyright information

© Springer 2012

Authors and Affiliations

  • Csaba Biró
    • 1
  • 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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