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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
Article

Abstract

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.

Keywords

Natural Generalization Edge Incident Local Coloring Monochromatic Copy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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