Abstract
The concept of a localk-coloring of a graphG is introduced and the corresponding localk-Ramsey numberr k loc (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 k loc (G) is the minimumm for whichK m contains a monochromatic copy ofG for every localk-coloring ofK m . The numberr k loc (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 k loc (G) for certain classes of graphs.
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Gyárfás, A., Lehel, J., Schelp, R.H. et al. Ramsey numbers for local colorings. Graphs and Combinatorics 3, 267–277 (1987). https://doi.org/10.1007/BF01788549
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DOI: https://doi.org/10.1007/BF01788549