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Chromatic numbers of exact distance graphs

van den Heuvel, Jan ORCID: 0000-0003-0897-9148, Kierstead, H. A and Quiroz, Daniel (2019) Chromatic numbers of exact distance graphs. Journal of Combinatorial Theory, Series B, 134. pp. 143-163. ISSN 0095-8956

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Identification Number: 10.1016/j.jctb.2018.05.007


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
Official URL:
Additional Information: © 2018 Elsevier Inc.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 31 May 2018 09:03
Last Modified: 20 Oct 2021 00:39
Projects: AFB170001
Funders: CONICYT, PIA/Concurso Apoyo a Centros Cientificos y Tecnologicos de Excelencia con Financiamiento Basal

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