Characterizing N+-perfect line graphs

ESCALANTE, MARIANA SILVINA; NASINI, GRACIELA LEONOR; WAGLER, ANNEGRET

Montevideo

Workshop; EURO ALIO Workshop on Applied and Combinatorial Optimization; 2014

ALIO-EURO IFORS

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 the PSD-operator 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.