Characterizing N+-perfect line graphs
Combinatorics
2015-05-18 v1
Abstract
The subject of this contribution is the study of the Lov\'asz-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.
Keywords
Cite
@article{arxiv.1505.04072,
title = {Characterizing N+-perfect line graphs},
author = {M. Escalante and G. Nasini and A. Wagler},
journal= {arXiv preprint arXiv:1505.04072},
year = {2015}
}