Matrix analysis
The mathematics of nonlinear programming
The mathematics of nonlinear programming
Semidefinite programming in combinatorial optimization
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Continuous characterizations of the maximum clique problem
Mathematics of Operations Research
On Standard Quadratic Optimization Problems
Journal of Global Optimization
Convex Quadratic Programming Approachto the Maximum Matching Problem
Journal of Global Optimization
SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0.
SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0.
An upper bound on the independence number of a graph computable in polynomial-time
Operations Research Letters
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In previous works an upper bound on the stability number of a graph based on quadratic programming was introduced and several of its properties were given. The graphs for which this bound is attained has been known as graphs with convex-QP stability number. This paper proposes a new upper bound on the stability number whose determination is also done by quadratic programming. It is proved that the new bound improves the above mentioned bound and several computational tests asserting its interest for large graphs are presented. In addition a necessary and sufficient condition for a graph to attain the new bound is proved. As a consequence a graph with convex-QP stability number also attains the new bound. On the other hand it is shown the existence of graphs attaining the new bound that do not belong to the class of graphs with convex-QP stability number. This allows to assert that the class of graphs with convex-QP stability number is strictly included in the class of graphs that attain the introduced bound. Some conclusions and lines for future work finalize the paper.