TORIC GEOMETRY OF SERIES-PARALLEL GRAPHS

Let G be a graph and K be a field. We associate to G a projective toric variety X-G over K, the cut variety of the graph G. The cut ideal I-G of the graph G is the ideal defining the cut variety. We show that, if G is a subgraph of a subdivision of a book or an outerplanar graph, then the minimal generators are quadrics. Furthermore, we describe the generators of the cut ideal of a subdivision of a book.