The toric ideal of a graphic matroid is generated by quadrics

Abstract

Describing minimal generating sets of toric ideals is a well-studied and difficult problem. Neil White conjectured in 1980 that the toric ideal associated to a matroid is generated by quadrics corresponding to single element symmetric exchanges. We give a combinatorial proof of White’s conjecture for graphic matroids.

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Correspondence to Jonah Blasiak.

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Blasiak, J. The toric ideal of a graphic matroid is generated by quadrics. Combinatorica 28, 283–297 (2008). https://doi.org/10.1007/s00493-008-2256-6

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Mathematics Subject Classification (2000)

  • 05B35
  • 05C05