Giving a partial solution to a problem of Bialostocki and Dierker, we determine the maximum number of edges in a k-chromatic graph G with color classes of given cardinalities n1,...nk, such that each connected component of G has at most p vertices, p|n1 + ⋯ + nk. We also characterize the extremal graphs and investigate to what extent their properties remain valid when multipartite r-uniform hypergraphs are considered.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics