An acyclic edge-coloring of a graph is a proper edge-coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph G is the minimum number k such that there is an acyclic edge-coloring using k colors and is denoted by χ′a(G). The maximum degree in G denoted by δ(G), is the lower bound for χ′a(G). We have introduced an architecture called Shuffle hypertree which is a variation of an hypertree. T-cuts introduced in this paper acts as a powerful tool to prove that this bound is sharp for hypertree and Shuffle hypertree. © 2015 Academic Publications, Ltd.