  We introduce the {\it Bipartite Multi-cut} problem. This is a generalization
of the {\it st-Min-cut} problem, is similar to the {\it Multi-cut} problem
(except for more stringent requirements) and also turns out to be an immediate
generalization of the {\it Min UnCut} problem. We prove that this problem is
{\bf NP}-hard and then present LP and SDP based approximation algorithms. While
the LP algorithm is based on the Garg-Vazirani-Yannakakis algorithm for {\it
Multi-cut}, the SDP algorithm uses the {\it Structure Theorem} of $\ell_2^2$
Metrics.
