Multipartite Turán problem for connected graphs and hypergraphs
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 (where \(n_ 1+...+n_ k\) is a multiple of p). We also characterize the extremal graphs and investigate to what extent their properties remain valid when multipartite r-uniform hypergraphs are considered. For hypergraphs, the general problem remains open.
scientific article; zbMATH DE number 4158658