Graphs and Combinatorics

, Volume 3, Issue 1, pp 267–277 | Cite as

Ramsey numbers for local colorings

  • A. Gyárfás
  • J. Lehel
  • R. H. Schelp
  • ZS. Tuza


The concept of a localk-coloring of a graphG is introduced and the corresponding localk-Ramsey numberr loc k (G) is considered. A localk-coloring ofG is a coloring of its edges in such a way that the edges incident to any vertex ofG are colored with at mostk colors. The numberr loc k (G) is the minimumm for whichK m contains a monochromatic copy ofG for every localk-coloring ofK m . The numberr loc k (G) is a natural generalization of the usual Ramsey numberr k (G) defined for usualk-colorings. The results reflect the relationship betweenr k (G) andr loc k (G) for certain classes of graphs.


Natural Generalization Edge Incident Local Coloring Monochromatic Copy 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • A. Gyárfás
    • 1
  • J. Lehel
    • 1
  • R. H. Schelp
    • 2
  • ZS. Tuza
    • 1
  1. 1.Computer and Automation InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.Memphis State UniversityMemphisUSA

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