The linear delta-matroid parity problem

Authors:
James F. Geelen;Satoru Iwata;Kazuo Murota
Affiliations:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo N2L 3G1, Canada;Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

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Abstract

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 delta-matroids. These are natural extensions of the minimax theorem of Lovász and the augmenting path algorithm of Gabow and Stallmann for the linear matroid parity problem.