Abstract
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 n 1,… n k , such that each connected component of G has at most p vertices, p| n 1 + ⋯ + n k . We also characterize the extremal graphs and investigate to what extent their properties remain valid when multipartite r-uniform hypergraphs are considered.
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