Symplectic Spaces And Ear-Decomposition Of Matroids

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.

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Correspondence to Balázs Szegedy.

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Szegedy, B., Szegedy, C. Symplectic Spaces And Ear-Decomposition Of Matroids. Combinatorica 26, 353–377 (2006). https://doi.org/10.1007/s00493-006-0020-3

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Mathematics Subject Classification (2000):

  • 05C70
  • 05C50
  • 05C85