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Two characterizations are given for a valuated delta-matroid. Let (V,F) be an even delta-matroid on a finite set V with the family F of feasible sets. It is shown that a function δ : F → R is a valuation of (V,F) if and only if, for each linear weighting p : V → R, the maximizers of δ+p form the family of feasible sets of a delta-matroid. It is also shown that δ is a valuation if and only if its conjugate function is “locally bisubmodular” at each point. (

CHARACTERIZING A VALUATED DELTA-MATROID AS A FAMILY OF DELTA-MATROIDS*