### Abstract

We study inverse chromatic number problems in permutation graphs and in interval graphs. Given a fixed instance and a fixed integer K, the instance has to be modified as little as possible so that the newly obtained graph can be colored with K colors or less. We show that the inverse (p, k)-colorability problem (defined similarly) in permutation graphs is polynomially solvable for fixed p and k. We then propose a polynomial-time algorithm for solving inverse chromatic number problem in interval graphs where all intervals have length 1 or 2. We also show that the latter problem is NP-hard if there is a constant number of different interval lengths.

Original language | English |
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Pages (from-to) | 1129-1136 |

Number of pages | 8 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 36 |

Issue number | C |

DOIs | |

Publication status | Published - 2010 Aug 1 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Electronic Notes in Discrete Mathematics*,

*36*(C), 1129-1136. https://doi.org/10.1016/j.endm.2010.05.143