Comparing invariants of toric ideals of bipartite graphs

Abstract

Let G G be a finite simple graph and let I G I_G denote its associated toric ideal in the polynomial ring R R . For each integer n ≥ 2 n\geq 2 , we completely determine all the possible values for the tuple ( reg ⁡ ( R / I G ) , deg ⁡ ( h R / I G ( t ) ) , pdim ⁡ ( R / I G ) , depth ⁡ ( R / I G ) , dim ⁡ ( R / I G ) ) (\operatorname {reg}(R/I_G), \deg (h_{R/I_G}(t)), \operatorname {pdim}(R/I_G), \operatorname {depth}(R/I_G), \dim (R/I_G)) when G G is a connected bipartite graph on n n vertices.