Abstract

It is NP-Hard to nd a proper 2-coloring of a given 2-colorable (bi- partite) hypergraph H. We consider algorithms that will color such a hypergraph using few colors in polynomial time. The results of the paper can be summarized as follows: Let n denote the number of vertices of H and m the number of edges. (i) For bipartite hypergraphs of dimension k there is a polynomial time algorithm which produces a proper coloring using minfO(n 1 1=k ); O((m=n) 1 k 1 )g colors. (ii) For 3-uniform bipartite hypergraphs, the bound is reduced to ~ O(n 2=9 ). (iii) For a class of dense 3-uniform bipartite hypergraphs, we have a randomized algorithm which can color optimally. (iv) For a model of random bipartite hypergraphs with edge probability p dn 2 , d > 0 a suciently large constant, we can almost surely nd a proper 2-coloring. 1 Introduction A hypergraph H = (V; E) has vertex set V; jV j = n, edge set E; jEj = m and each edge e 2 E is simply a subset of V . Its dimension dim(H) is...

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