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

Authors:
Hans-JüRgen Bandelt;Maarten Oosten;Jeroen H. G. C. Rutten;Frits C. R. Spieksma
Affiliations:
Mathematisches Seminar, Universität Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany;Faculty of Commerce and Business Administration, 2053 Main Mall, Vancouver, BC, Canada V6T 1Z2;ASM Lithography, P.O. Box 324, NL-5500 AH Veldhoven, The Netherlands;Department of Mathematics, Maastricht University, P.O. Box 616, NL-6200 MD Maastricht, The Netherlands
Venue:
Operations Research Letters
Year:
1999

Citing 3
Cited 3

Integer and combinatorial optimization

Integer and combinatorial optimization
Facets of the clique partitioning polytope

Mathematical Programming: Series A and B
The partition problem

Mathematical Programming: Series A and B

Facet-defining inequalities for the simple graph partitioning polytope

Discrete Optimization
A mixed integer programming model for the parsimonious loss of heterozygosity problem

ISBRA'12 Proceedings of the 8th international conference on Bioinformatics Research and Applications
An Integer Programming Formulation of the Parsimonious Loss of Heterozygosity Problem

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)

Quantified Score

Hi-index	0.00

Visualization

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 K"m on m vertices, it defines a facet for the polytope corresponding to K"n for all nm. This answers a question raised by Grotschel and Wakabayashi. Further, for the case of arbitrary graphs, we characterize when the so-called 2-partition inequalities define facets.