On minimum cuts and the linear arrangement problem Original Research Article

In this paper we examine the problem of finding minimum cuts in finite graphs with the side constraint that the vertex sets inducing these cuts must be of a given cardinality. As it turns out, this computation is of interest not only from a combinatorial perspective but also from a practical one, pertaining to the linear arrangement value of graphs. We look at some graph classes where these cuts can be efficiently computed (in general this computation is NP-hard) as well as some cases where their value can be determined in closed form.