## Abstract

We present exact calculations of the partition function of the zero-temperature Potts antiferromagnet (equivalently, the chromatic polynomial) for graphs of arbitrarily great length composed of repeated complete subgraphs K_{b} with b=5, 6 which have periodic or twisted periodic boundary condition in the longitudinal direction. In the L_{x} → ∞ limit, the continuous accumulation set of the chromatic zeros ℬ is determined. We give some results for arbitrary b including the extrema of the eigenvalues with coefficients of degree b-1 and the explicit forms of some classes of eigenvalues. We prove that the maximal point where ℬ crosses the real axis, q_{c}, satisfies the inequality q_{c} ≤ b for 2 ≤ b, the minimum value of q at which ℬ crosses the real q axis is q = 0, and we make a conjecture concerning the structure of the chromatic polynomial for Klein bottle strips.

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

Pages (from-to) | 397-426 |

Number of pages | 30 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 313 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2002 Oct 15 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics