Coloring bipartite hypergraphs

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Abstract

It is NP-Hard to find a proper 2-coloring of a given 2-colorable (bipartite) 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 min (formula presented) colors, (ii) For 3-uniform bipartite hypergraphs, the bound is reduced to O(n2/9). (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 > O a sufficiently large constant, we can almost surely find a proper 2-coloring.

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Chen, H., & Frieze, A. (1996). Coloring bipartite hypergraphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1084, pp. 345–358). Springer Verlag. https://doi.org/10.1007/3-540-61310-2_26

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