Maximum Weight Stable Set Problem Research Articles

Binary integer programs with two variables per inequality

Several recent papers have shown that some properties of the maximum weight stable set problem hold true in the more general setting of binary integer programs with two variables per inequality. In this paper, we show that in fact the two problems are equivalent by using the transitive closure of the binary integer program and (possibly) reducing the number of variables by fixing, complementing, or identifying them. We use this equivalence to prove two conjectures made by Johnson and Padberg regarding the perfection of bidirected graphs.

A note on line digraphs and the directed max-cut problem

The support of a digraph is the undirected graph arising when directions of edges are ignored. We prove that recognizing supports of line digraphs of digraphs is an NP-Complete problem. Then we observe that solvable cases of the directed max-cut problem arise from solvable cases of the maximum-weight stable set problem via supports of line digraphs; in particular, we investigate digraphs G such that the support of the line digraph of G is perfect.