### 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

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*Electronic Notes in Discrete Mathematics*, vol. 36, no. C, pp. 1129-1136. https://doi.org/10.1016/j.endm.2010.05.143

**On inverse chromatic number problems (Extended abstract).** / Chung, Yerim; Culus, Jean François; Demange, Marc.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On inverse chromatic number problems (Extended abstract)

AU - Chung, Yerim

AU - Culus, Jean François

AU - Demange, Marc

PY - 2010/8/1

Y1 - 2010/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77954949804&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954949804&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2010.05.143

DO - 10.1016/j.endm.2010.05.143

M3 - Article

AN - SCOPUS:77954949804

VL - 36

SP - 1129

EP - 1136

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

IS - C

ER -