APPLICATIONS OF GR ¨ OBNER BASES IN GRAPH THEORY

The theory of Gr¨obner bases was developed by B. Buchberger in 1965, in the context of his PhD thesis, who named them after his advisor W. Gr¨obner. A Gr¨obner basis is a particular kind of generating set for a polynomial ideal, and it can be considered as a non-linear generalization of Gaussian elimination for linear systems. The method of Gr¨obner bases is a powerful technique that provides algorithmic solutions to a variety of problems in commutative algebra and algebraic geometry. In this talk, we give a brief overview on the theory of Gr¨obner bases and review some of its applications in graph