Chromatic numbers of exact distance graphs

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
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 May 2020 00:24
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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