A Binomial Ideal on Triangulations of-2

Abstract

In this paper, we introduce a binomial ideal P(Tn) on a simple graph Tn obtained from n−triangulation of a 2−manifols. It is discussed on two particular classes of n−triangulation graphs: the class Tn1 and the class Tn2 . The Gro¨bner bases of the binomial ideals P(Tn1 ) and P(Tn2 ) on n1−triangulation and n2−triangulation graphs Tn1 and Tn2 respectively are computed using a systematic way and it is shown that degree of polynomials in the Gro¨bner bases of these n−triangulation graphs is at most 5. Also, it is shown that the binomial ideals P(Tn1 ) and Tn2 are regular ideals.