Maximum-weight stable sets and safe lower bounds for graph coloring

  title={Maximum-weight stable sets and safe lower bounds for graph coloring},
  author={Stephan Held and William J. Cook and Edward C. Sewell},
  journal={Math. Program. Comput.},
The best method known for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique, where variables correspond to stable sets, first employed by Mehrotra and Trick in 1996. We present an implementation of the method that provides numerically-safe results, independent of the floating-point accuracy of linear-programming software. Our work includes an improved branch-andbound algorithm for maximum-weight stable sets and a parallel… CONTINUE READING
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