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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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Identification Number: 10.1016/j.jctb.2018.05.007

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 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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