The Cycling Property for the Clutter of Odd st-Walks
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چکیده
A binary clutter is cycling if its packing and covering linear program have integral optimal solutions for all Eulerian edge capacities. We prove that the clutter of odd stwalks of a signed graph is cycling if and only if it does not contain as a minor the clutter of odd circuits of K5 nor the clutter of lines of the Fano matroid. Corollaries of this result include, of many, the characterization for weakly bipartite signed graphs [5], packing twocommodity paths [7, 11], packing T -joins with small |T |, a new result on covering odd circuits of a signed graph, as well as a new result on covering odd circuits and odd T -joins of a signed graft.
منابع مشابه
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A binary clutter is the family of odd circuits of a binary matroid, that is, the family of circuits that intersect with odd cardinality a fixed given subset of elements. Let A denote the 0;1 matrix whose rows are the characteristic vectors of the odd circuits. A binary clutter is ideal if the polyhedron fx 0 : Ax 1g is integral. Examples of ideal binary clutters are st-paths, st-cuts, T -joins ...
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