“…, y n ], where K is a field. The connection between combinatorial invariants associated to G and algebraic invariants associated to J G has been of intense study in the past one decade (see [1,3,4,6,9,10,14,16,17,18] for a partial list). In [1], Banerjee and Núñez Betancourt proved that for a connected non-complete graph G, depth(S/J G ) ≤ n + 2 − κ(G), where κ(G) = min{|T | : T ⊂ [n] and G [n]\T is disconnected} is the graph connectivity.…”