The maximal generating degree of the Eulerian ideal

In commutative algebra, a major subject of investigation is the study of ideals in polynomial rings that are defined by graphs; the goal is to understand how the properties of the ideals relate to the properties of the associated graphs. One of the several ideals studied in this context is the Eulerian ideal of a graph G. This ideal is generated by binomials which identify Eulerian subgraphs of G with an even number of edges. In this talk, we characterize the binomials that belong to a minimal homogeneous generating set of the Eulerian ideal and, for some families of graphs, we determine the greatest degree of these binomials.