GRAPHS AND IDEALS GENERATED BY SOME 2-MINORS

Let G be a finite graph on [n] = {1, 2, ... , n}, X a 2 x n matrix of indeterminates over a field K, and S = K[X] 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 Grobner basis of I-G as a set of paths of G and compute a primary decomposition.