Frame Matroids, Toric Ideals, and a Conjecture of White

2019/10/18 by McGuinness, Sean · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.08587

Abstract

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.

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• Matroids are Equitable
• Hamiltonian connectivity of some base-cobase graphs

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