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Connectedness of the graph of vortex-colourings

Cereceda, Luis, van den Heuvel, Jan and Johnson, Matthew (2005) Connectedness of the graph of vortex-colourings. CDAM research report series, CDAM-LSE-2005-11. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

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Abstract

For a positive integer k and a graph G, the k-colour graph of G, Ck(G), is the graph that has the proper k-vertex-colourings of G as its vertex set, and two k-colourings are joined by an edge in Ck(G) if they differ in colour on just one vertex of G. In this note some results on the connectivity of Ck(G) are proved. In particular it is shown that if G has chromatic number k 2 {2, 3}, then Ck(G) is not connected. On the other hand, for k ¸ 4 there are graphs with chromatic number k for which Ck(G) is not connected, and there are k-chromatic graphs for which Ck(G) is connected.

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk
Additional Information: © 2005 the authors
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: CDAM-LSE-2005-11
Date Deposited: 27 Oct 2008 14:18
URL: http://eprints.lse.ac.uk/13886/

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