## Abstract

For each integer n5 and each rational number r in the interval [2,n-1], we construct a K _{n}-minor free graph G with χ _{c}(G)=r. This answers a question asked by Zhu (Discrete Mathematics, 229 (1-3) (2001) 371). In case n=5, the constructed graphs are actually planar. Such planar graphs were first constructed in J. Graph Theory 24 (1997) 33 (for ∈[2,3]) and in J. Combin. Theory 76 (1999) 170 (for r∈[3,4]). However, our construction and proof are much simpler.

Original language | English |
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Pages (from-to) | 191-206 |

Number of pages | 16 |

Journal | Discrete Mathematics |

Volume | 263 |

Issue number | 1-3 |

DOIs | |

State | Published - 28 Feb 2003 |

## Keywords

- Circular chromatic number
- Hadwiger conjecture
- K -minor free graphs
- Planar graphs
- Series-parallel construction

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