Coloring the Edges of A Hypergraph and Linear Programming Techniques

Abstract

A theorem of Baranyai reduces the problem of finding the chromatic index of certain hypergraphs to a cutting stock integer programming problem. Baranyai used this result to establish the chromatic index for the complete h -uniform hypergraphs. We use a linear programming technique of Gomory and Gilmore to extend his result to two other cases: the hereditary closure of the complete h -uniform hypergraphs K h n , for h ≤ 4; and of the complete h -partite hypergraphs.