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

doi:10.1016/S0167-6377(99)00029-2

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

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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 language	English
Pages (from-to)	235-243
Journal	Operations Research Letters
Volume	24
DOIs	https://doi.org/10.1016/S0167-6377(99)00029-2
Publication status	Published - 1999
Externally published	Yes

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title = "Lifting theorems and facet characterization for a class of clique partitioning inequalities",

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 Gr{\"o}tschel and Wakabayashi. Further, for the case of arbitrary graphs, we characterize when the so-called 2-partition inequalities define facets",

author = "H.J. Bandelt and M. Oosten and J.H.G.C. Rutten and F.C.R. Spieksma",

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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

SN - 0167-6377

VL - 24

SP - 235

EP - 243

JO - Operations Research Letters

JF - Operations Research Letters

ER -

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

Abstract

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