Lovasz-Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs

• 成果类型: Article
• 署名作者: Bianchi, S.; Escalante, M.; Nasini, G.; Tuncel, L.
• 署名单位: National University of Rosario; University of Waterloo
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1035-1
• 发表日期: 2017
• 页码: 201-223
• 关键词: stable set problem; stability number; optimization; polytopes; matrices; progress

摘要

We study the Lovasz-Schrijver lift-and-project operator () 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 -operator generates the stable set polytope in one step has been open since 1990. We call these graphs -perfect. In the current contribution, we pursue a full combinatorial characterization of -perfect graphs and make progress towards such a characterization by establishing a new, close relationship among -perfect graphs, near-bipartite graphs and a newly introduced concept of full-support-perfect graphs.