Before revision:  Bencz\'ur and Karger, STOC 1996) , then we show that the size of the sparsifier (or even cut sketch) must scale linearly with \beta. The upper bound is a simple extension of sparsification of undirected graphs (formally stated recently in Ikeda and Tanigawa (WAOA 2018)), so our main contribution here is to show a matching lower bound. For-Each Sparsification: If each cut value needs to be individually preserved ( Andoni et al., ITCS 2016) , then the situation is more interesting.
After revision:  Bencz\'ur and Karger, STOC 1996) and for-each ( Andoni et al., ITCS 2016) , then the situation is more interesting.