  Blasiak verified a conjecture of White for graphic matroids by showing that
the toric ideal of a graphic matroid is generated by quadrics. In this paper,
we extend this result to frame matroids satisfying a linearity condition. Such
classes of matroids include graphic matroids, bicircular matroids, signed
graphic matroids, and more generally frame matroids obtained from
group-labelled graphs.
