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This paper addresses a generalization of the matroid parity problem to delta-matroids. We give a minimax relation, as well as an efficient algorithm, for linearly represented deltamatroids. These are natural extensions of the minimax theorem of Lova´sz and the augmenting path algorithm of Gabow and Stallmann for the linear matroid parity problem. rdoi:10.1016/s0095-8956(03)00039-x fatcat:r7fmsok5hzbydmii6wsm26po3m