We compute a complete linear description of the bipartite subgraph polytope, for up to seven nodes, and a conjectured complete description for eight nodes. We then show how these descriptions were used to compute the integrality ratio of various relaxations of the max-cut problem, again for up to eight nodes

Adam N. Letchford

Barahona

Christof

Delorme

Deza

Feige

Goemans

Grishukhin

Grötschel

Karp

Laura Galli

Laurent

Poljak

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Archivio della Ricerca - Università di Pisa

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English

All facets of the cut cone for n D 7 are known,

Decomposition and parallelization techniques for enumeratingthefacetsofcombinatorialpolytopes,Int.J.Comput.Geom.Appl. 11

Facets for the cut cone (parts I and II),

Facets of the bipartite subgraph polytope,

Geometry of Cuts and Metrics,

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Laplacian eigenvalues and the maximum cut problem,

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PORTA (polyhedron representation transformation algorithm). Software package, available for download at http://www.zib.de/ Optimization/Software/Porta/.

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The strongest facets of the acyclic subgraph polytope are unknown, in:

The unique games conjecture, integrality gap for cut problems and embeddability of negative type metrics into `1, in:

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Weakly bipartite graphs and the max-cut problem,

Small bipartite subgraph polytopes