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Let G be a finite graph on n = 1, 2, …, n, X a 2 × n matrix of indeterminates over a field K, and S = KX a polynomial ring over K. In this article, we study about ideals I G of S generated by 2-minors i, j of X which correspond to edges i, j of G. In particular, we construct a Gröbner basis of I G as a set of paths of G and compute a primary decomposition.
Masahiro Ohtani (Wed,) studied this question.