### Abstract

^{6}+4(t-1)

^{2}(t-2)

^{3}-(t-1)

^{4}. We also construct a family of graphs containing such spanning trees with chromatic roots converging to t1 from above. We employ the Whitney 2-switch operation to manage the analysis of an infinite class of chromatic polynomials.

Original language | English |
---|---|

Journal | Discrete Mathematics |

Volume | 339 |

Issue number | 11 |

Pages (from-to) | 2706-2714 |

ISSN | 0012-365X |

DOIs | |

Publication status | Published - 2016 |

### Keywords

- Chromatic polynomial
- Zero-free interval
- Spanning tree
- Splitting-closed

### Cite this

*Discrete Mathematics*,

*339*(11), 2706-2714. https://doi.org/10.1016/j.disc.2016.05.009

}

*Discrete Mathematics*, vol. 339, no. 11, pp. 2706-2714. https://doi.org/10.1016/j.disc.2016.05.009

**A zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees.** / Perrett, Thomas.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - A zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees

AU - Perrett, Thomas

PY - 2016

Y1 - 2016

N2 - It is proved that if G is a graph containing a spanning tree with at most three leaves, then the chromatic polynomial of G has no roots in the interval (1,t1], where t1≈1.2904 is the smallest real root of the polynomial (t-2)6+4(t-1)2 (t-2)3-(t-1)4. We also construct a family of graphs containing such spanning trees with chromatic roots converging to t1 from above. We employ the Whitney 2-switch operation to manage the analysis of an infinite class of chromatic polynomials.

AB - It is proved that if G is a graph containing a spanning tree with at most three leaves, then the chromatic polynomial of G has no roots in the interval (1,t1], where t1≈1.2904 is the smallest real root of the polynomial (t-2)6+4(t-1)2 (t-2)3-(t-1)4. We also construct a family of graphs containing such spanning trees with chromatic roots converging to t1 from above. We employ the Whitney 2-switch operation to manage the analysis of an infinite class of chromatic polynomials.

KW - Chromatic polynomial

KW - Zero-free interval

KW - Spanning tree

KW - Splitting-closed

U2 - 10.1016/j.disc.2016.05.009

DO - 10.1016/j.disc.2016.05.009

M3 - Journal article

VL - 339

SP - 2706

EP - 2714

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 11

ER -