Handbook of combinatorics (vol. 1)
Continuous characterizations of the maximum clique problem
Mathematics of Operations Research
On Standard Quadratic Optimization Problems
Journal of Global Optimization
An upper bound on the independence number of a graph computable in polynomial-time
Operations Research Letters
Improving an Upper Bound on the Stability Number of a Graph
Journal of Global Optimization
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The problem of determining a maximum matching or whether there exists a perfect matching, is very common in a large variety of applications and as been extensively studied in graph theory. In this paper we start to introduce a characterisation of a family of graphs for which its stability number is determined by convex quadratic programming. The main results connected with the recognition of this family of graphs are also introduced. It follows a necessary and sufficient condition which characterise a graph with a perfect matching and an algorithmic strategy, based on the determination of the stability number of line graphs, by convex quadratic programming, applied to the determination of a perfect matching. A numerical example for the recognition of graphs with a perfect matching is described. Finally, the above algorithmic strategy is extended to the determination of a maximum matching of an arbitrary graph and some related results are presented.