Characterizing N+‐perfect line graphs. (21st March 2016)

• Record Type: Journal Article
• Authors: Escalante, Mariana; Nasini, Graciela; Wagler, Annegret
• Other Names: Cancela Héctor guestEditor.; Martins Simone guestEditor.; Mauttone Antonio guestEditor.; Urquhart María E. guestEditor.
• Is Part Of: International transactions in operational research. Volume 24:Number 1/2(2017)
• Page Start: 325
• Page End: 337
• Publication Date: 2016-03-21
• Subjects: stable set polytope -- N+‐perfect graphs -- line graphs -- PSD relaxation; Operations research -- Periodicals; 003
• DOI: 10.1111/itor.12275
• Languages: English
• ISSNs: 0969-6016

Abstract

Abstract: The aim of this paper is to study the Lovász‐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 subgraphs are cliques and odd holes.