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The toric ideal of a graphic matroid is generated by quadrics

Jonah Blasiak
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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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Jonah Blasiak. 2005-11-09. The toric ideal of a graphic matroid is generated by quadrics. https://arxiv.org/abs/math/0511223

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