Lifting theorems and facet characterization for a class of clique partitioning inequalities

H.J. Bandelt, M. Oosten, J.H.G.C. Rutten, F.C.R. Spieksma

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this paper we prove two lifting theorems for the clique partitioning polytope, which provide sufficient conditions for a valid inequality to be facet-defining. In particular, if a valid inequality defines a facet of the polytope corresponding to the complete graph Km on m vertices, it defines a facet for the polytope corresponding to Kn for all n>m. This answers a question raised by Grötschel and Wakabayashi. Further, for the case of arbitrary graphs, we characterize when the so-called 2-partition inequalities define facets
Original languageEnglish
Pages (from-to)235-243
JournalOperations Research Letters
Volume24
DOIs
Publication statusPublished - 1999
Externally publishedYes

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Clique
Facet
Partitioning
Polytope
Valid Inequalities
Theorem
Complete Graph
Partition
Class
Valid inequalities
Graph
Sufficient Conditions
Arbitrary
Graph in graph theory

Cite this

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Lifting theorems and facet characterization for a class of clique partitioning inequalities. / Bandelt, H.J.; Oosten, M.; Rutten, J.H.G.C.; Spieksma, F.C.R.

In: Operations Research Letters, Vol. 24, 1999, p. 235-243.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Lifting theorems and facet characterization for a class of clique partitioning inequalities

AU - Bandelt, H.J.

AU - Oosten, M.

AU - Rutten, J.H.G.C.

AU - Spieksma, F.C.R.

PY - 1999

Y1 - 1999

N2 - In this paper we prove two lifting theorems for the clique partitioning polytope, which provide sufficient conditions for a valid inequality to be facet-defining. In particular, if a valid inequality defines a facet of the polytope corresponding to the complete graph Km on m vertices, it defines a facet for the polytope corresponding to Kn for all n>m. This answers a question raised by Grötschel and Wakabayashi. Further, for the case of arbitrary graphs, we characterize when the so-called 2-partition inequalities define facets

AB - In this paper we prove two lifting theorems for the clique partitioning polytope, which provide sufficient conditions for a valid inequality to be facet-defining. In particular, if a valid inequality defines a facet of the polytope corresponding to the complete graph Km on m vertices, it defines a facet for the polytope corresponding to Kn for all n>m. This answers a question raised by Grötschel and Wakabayashi. Further, for the case of arbitrary graphs, we characterize when the so-called 2-partition inequalities define facets

U2 - 10.1016/S0167-6377(99)00029-2

DO - 10.1016/S0167-6377(99)00029-2

M3 - Article

VL - 24

SP - 235

EP - 243

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

ER -