Let d, k be any two positive integers with k > d > 0. We consider a k-coloring of a graph G such that the distance between each pair of vertices in the same color-class is at least d. Such graphs are said to be (k,d)-colorable. The object of this paper is to determine the maximum size of (k,3)-colorable, (k,4)-colorable, and (k,k-1)-colorable graphs. Sharp results are obtained for both (k,3)-colorable and (k,k-1)-colorable graphs, while the results obtained for (k,4)-colorable graphs are close to the truth.
- Chromatic number
- Extremal number
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics