Characterizing a valuated delta-matroid as a family of deltamatroids, Report No

Abstract Two characterizations are given for a valuated delta-matroid. Let ( V, 3) be an even delta-matroid on a finite set V with the family 3 of feasible sets. I t is shown that a function S: T-+ R is a valuation of (V, 3) if and only if, for each linear weighting p: V Ã ‘ R, the maximizers of S + p form the family of feasible sets of a delta-matroid. It is also shown that S is a valuation if and only if its conjugate function is "locally bisubmodular " a t each point. 1