### Abstract

Given an edge-weighted graph and an integer k, the generalized graph coloring problem is the problem of partitioning the vertex set into k subsets so as to minimize the total weight of the edges that are included in a single subset. We recall a result on the equivalence between karush–kuhn–tucker points for a quadratic programming formulation and local optima for the simple flip-neighborhood. We also show that the quality of local optima with respect to a large class of neighborhoods may be arbitrarily bad and that some local optima may be hard to find.

Original language | English |
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Pages (from-to) | 28-34 |

Journal | Operations Research Letters |

Volume | 31 |

DOIs | |

Publication status | Published - 1 Jan 2003 |

## Cite this

Vredeveld, T., & Lenstra, J. K. (2003). On local search for the generalized graph coloring problem,

*Operations Research Letters*,*31*, 28-34. https://doi.org/10.1016/S0167-6377(02)00165-7