Characterizing N+-perfect line graphs

Abstract

The aim of this paper is to study the Lovász-Schrijver PSD operator N+ applied to the edge relaxation of the stable set polytope of a graph. We are particularly interested in the problem of characterizing graphs for which N+ generates the stable set polytope in one step, called N+ -perfect graphs. It is conjectured that the only N+ -perfect graphs are those whose stable set polytope is described by inequalities with near-bipartite support. So far, this conjecture has been proved for near-perfect graphs, fs-perfect graphs, and webs. Here, we verify it for line graphs, by proving that in an N+ -perfect line graph the only facet-defining subgraphs are cliques and odd holes.