2015/05/15 by Escalante, M., Nasini, G., Wagler, A.
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1505.04072
The subject of this contribution is the study of 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 graphs are cliques and odd holes.