Local k-colorings of graphs and hypergraphs

A local k-coloring of a graph is a coloring of its edges in such a way that each vertex is incident to edges of at most k different colors. We investigate the similarities and differences between usual and local k-colorings, and the results presented in the paper give a general insight to the nature of local colorings. We are mainly concerned with local variants of Ramsey-type problems, in particular, with Ramsey's theorem for hypergraphs, the existence of minimal Ramsey graphs and further questions from noncomplete Ramsey Theory. © 1987 Academic Press, Inc.