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arXiv · 1505.04072

Characterizing N+-perfect line graphs

M. Escalante·G. Nasini·A. Wagler
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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.

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M. Escalante, G. Nasini, A. Wagler. 2015-05-15. Characterizing N+-perfect line graphs. https://arxiv.org/abs/1505.04072

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