The toric ideal of a graphic matroid is generated by quadrics

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.

• Type: Journal
• Year: 2008
• Where: COMBINATORICA
• Authors: Jonah Blasiak
• Keywords: COMBINATORICA 2008, Element Symmetric Exchanges, Minimal Generating Sets, Toric Ideal