Linear time algorithms for finding sparsest cuts in various graph classes

[ S , S ¯ ] denotes the set of edges with exactly one end vertex in S. The density of an edge cut [ S , S ¯ ] is | [ S , S ¯ ] | / ( | S | | S ¯ | ) . A sparsest cut is an edge cut with minimum density. We characterize the sparsest cuts for unit interval graphs, complete bipartite graphs and cactus graphs. For all of these classes, the characterizations lead to linear time algorithms to find a sparsest cut.