### Abstract

Given a graph G and a positive integer K, the inverse chromatic number problem consists in modifying the graph as little as possible so that it admits a chromatic number not greater than K. In this paper, we focus on the inverse chromatic number problem for certain classes of graphs. First, we discuss diverse possible versions and then focus on two application frameworks which motivate this problem in interval and permutation graphs: the inverse booking problem and the inverse track assignment problem. The inverse booking problem is closely related to some previously known scheduling problems; we propose new hardness results and polynomial cases. The inverse track assignment problem motivates our study of the inverse chromatic number problem in permutation graphs; we show how to solve in polynomial time a generalization of the problem with a bounded number of colors.

Original language | English |
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Pages (from-to) | 763-773 |

Number of pages | 11 |

Journal | European Journal of Operational Research |

Volume | 243 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 Jun 16 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Modelling and Simulation
- Management Science and Operations Research
- Information Systems and Management

### Cite this

*European Journal of Operational Research*,

*243*(3), 763-773. https://doi.org/10.1016/j.ejor.2014.12.028