Edge Coloring Complete Uniform Hypergraphs with Many Components

Let be a hypergraph. For a -edge coloring let (, ) be the number of components in the subhypergraph induced by the color class with the least number of components. Let () be the maximum possible value of (, ) ranging over all k-edge colorings of . If is the complete graph then, trivially, . In this paper we prove that for ≥ 6, and supply close upper and lower bounds for () in case ≥ 4. Several results concerning the value of , where is the complete -uniform hypergraph on vertices, are also established