Symplectic Spaces And Ear-Decomposition Of Matroids
- Cite this article as:
- Szegedy, B. & Szegedy, C. Combinatorica (2006) 26: 353. doi:10.1007/s00493-006-0020-3
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Matroids admitting an odd ear-decomposition can be viewed as natural generalizations of factor-critical graphs. We prove that a matroid representable over a field of characteristic 2 admits an odd ear-decomposition if and only if it can be represented by some space on which the induced scalar product is a non-degenerate symplectic form. We also show that, for a matroid representable over a field of characteristic 2, the independent sets whose contraction admits an odd ear-decomposition form the family of feasible sets of a representable Δ-matroid.