@article{Bollobs2000LocalAM,
title={Local and Mean Ramsey Numbers for Trees},
author={B{\'e}la Bollob{\'a}s and Alexandr V. Kostochka and Richard H. Schelp},
journal={J. Comb. Theory, Ser. B},
year={2000},
volume={79},
pages={100-103}
}

The usual Ramsey number R(G, k) is the smallest positive integer n such that any coloring of the edges of Kn by at most k colors contains a monochromatic copy of G. Over the past years several papers have been written in which the number of different colors used has no longer been restricted to k, but a restriction is placed on the number of colored edges incident to the vertices. To be precise, let H be a fixed graph of order n and let f be a coloring on the edges of H. For each v # V(H… CONTINUE READING