### Abstract

For a simple graph of maximum degree Δ, the complexity of computing the fractional total chromatic number is unknown. Trivially it is at least Δ + 1. Kilakos and Reed proved that it is at most Δ + 2. In this paper, we strengthen this by characterizing exactly those simple graphs with fractional total chromatic number Δ + 2. This yields a simple linear-time algorithm to determine whether a given graph has fractional chromatic number Δ + 2. Crown

Original language | English |
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Pages (from-to) | 235-240 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 35 |

Issue number | C |

DOIs | |

Publication status | Published - 2009 Dec 1 |

### Keywords

- edge colouring
- fractional total colouring
- graph theory

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Ito, T., Kennedy, W. S., & Reed, B. A. (2009). A Characterization of Graphs with Fractional Total Chromatic Number Equal to Δ + 2.

*Electronic Notes in Discrete Mathematics*,*35*(C), 235-240. https://doi.org/10.1016/j.endm.2009.11.039