Biclique coverings of regular bigraphs and minimum semiring ranks of regular matrices
نویسندگان
چکیده
We study the minimum number of complete bipartite subgraphs needed to cover and partition the edges of a k-regular bigraph on 2n vertices. Bounds are determined on the minima of these numbers for fixed n and k. Exact values of the minima are found for all n and k 6 4. The same results hold for directed graphs. Equivalently, we have determined bounds on the minimum value of the Boolean and nonnegative integer ranks of binary n xn matrices with constant row and column sum k for fixed n and k, obtaining the exact values of the minimum for k <4.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 51 شماره
صفحات -
تاریخ انتشار 1991