Small bipartite subgraph polytopes

Authors:
Laura Galli;Adam N. Letchford
Affiliations:
University of Bologna, Italy;Department of Management Science, Lancaster University, Lancaster LA1 4YW, United Kingdom
Venue:
Operations Research Letters
Year:
2010

Citing 9
Cited 1

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All facets of the cut Cn for n = 7 are known

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Facets for the cut cone I

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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

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On the optimality of the random hyperplane rounding technique for max cut

Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
The Strongest Facets of the Acyclic Subgraph Polytope Are Unknown

Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into \ell 1

FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Weakly bipartite graphs and the Max-cut problem

Operations Research Letters

Gap inequalities for the max-cut problem: a cutting-plane algorithm

ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization

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Abstract

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.