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Graphs and Combinatorics

, Volume 2, Issue 1, pp 55–60 | Cite as

Coloring of universal graphs

  • Peter Komjáth
  • Vojtèch Rödl
Article

Abstract

LetG be a graph andr a cardinal number. Extending the theorem of J. Folkman we show that if eitherr or clG are finite then there existsH with clH = clG andH → (G) r 1 . Answering a question of A. Hajnal we show that countably universal graphU3 satisfiesU3 → (U3) r 1 for every finiter.

Keywords

Cardinal Number Universal Graph 
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References

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Peter Komjáth
    • 1
  • Vojtèch Rödl
    • 2
    • 3
  1. 1.Department of MathematicsEötvös UniversityBudapestHungary
  2. 2.Department of MathematicsFJFI ČVUTPraha 1Czechoslovakia
  3. 3.AT&T Bell LaboratoriesMurray HillUSA

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