van den Heuvel, Jan, Kierstead, H. A and Quiroz, Daniel
(2018)
*Chromatic numbers of exact distance graphs.*
Journal of Combinatorial Theory, Series B.
ISSN 0095-8956

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## Abstract

For any graph G = (V;E) and positive integer p, the exact distance-p graph G[\p] is the graph with vertex set V , which has an edge between vertices x and y if and only if x and y have distance p in G. For odd p, Nešetřil and Ossona de Mendez proved that for any fixed graph class with bounded expansion, the chromatic number of G[\p] is bounded by an absolute constant. Using the notion of generalised colouring numbers, we give a much simpler proof for the result of Nešetřil and Ossona de Mendez, which at the same time gives significantly better bounds. In particular, we show that for any graph G and odd positive integer p, the chromatic number of G[\p] is bounded by the weak (2p

Item Type: | Article |
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Official URL: | https://www.journals.elsevier.com/journal-of-combi... |

Additional Information: | © 2018 Elsevier Inc. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 31 May 2018 09:03 |

Last Modified: | 20 Feb 2019 06:48 |

Projects: | AFB170001 |

Funders: | CONICYT, PIA/Concurso Apoyo a Centros Cientificos y Tecnologicos de Excelencia con Financiamiento Basal |

URI: | http://eprints.lse.ac.uk/id/eprint/88134 |

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