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arXiv · 1411.2069

Lov\'asz-Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs

S. Bianchi·M. Escalante·G. Nasini·L. Tunçel
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Abstract

We study the Lov\'asz-Schrijver lift-and-project operator ($LS_+$) based on the cone of symmetric, positive semidefinite matrices, applied to the fractional stable set polytope of graphs. The problem of obtaining a combinatorial characterization of graphs for which the $LS_+$-operator generates the stable set polytope in one step has been open since 1990. We call these graphs $LS_+$-perfect. In the current contribution, we pursue a full combinatorial characterization of $LS_+$-perfect graphs and make progress towards such a characterization by establishing a new, close relationship among $LS_+$-perfect graphs, near-bipartite graphs and a newly introduced concept of full-support-perfect graphs.

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S. Bianchi, M. Escalante, G. Nasini, L. Tunçel. 2014-11-08. Lov\'asz-Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs. https://arxiv.org/abs/1411.2069

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