Let G be a graph, m>r≥1 integers. Suppose that it has a good coloring with m colors which uses at most r colors in the neighborhood of every vertex. We investigate these so-called local r-colorings. One of our results (Theorem 2.4) states: The chromatic number of G, Chr(G)≤r2rlog2log2 m (and this value is the best possible in a certain sense). We consider infinite graphs as well.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics