Optimization Letters

, Volume 10, Issue 1, pp 19–31

# A characterization of the weighted Lovász number based on convex quadratic programming

• Carlos J. Luz
Original Paper

## Abstract

Luz and Schrijver (SIAM J Discrete Math 19(2):382–387, 2005) introduced a characterization of the Lovász number based on convex quadratic programming. This characterization is now extended to the weighted version of that number. In consequence, a class of graphs for which the weighted Lovász number coincides with the weighted stability number is characterized. Several examples of graphs of this class are presented.

## Keywords

Weighted Lovász number Maximum weight stable set  Combinatorial optimization Graph theory Quadratic programming

## Notes

### Acknowledgments

The author thanks the referees for their helpful comments and suggestions which improved the paper. This research was supported by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA) and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e Tecnologia”), within project UID/MAT/04106/2013.

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