  In communication field, an important issue is to group users and base
stations to as many as possible subnetworks satisfying certain interference
constraints. These problems are usually formulated as a graph partition
problems which minimize some forms of graph cut. Previous research already gave
some results about the cut bounds for unweighted regular graph. In this paper,
we prove a result about the lower bound for weighted graphs that have some
regular properties and show similar results for more general case.
