The toric ideal of a graphic matroid is generated by quadrics
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toricgeneratedgraphicidealmatroidquadricswhiteassociated
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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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