Gray code numbers for graphs

Kelly Choo, Gary MacGillivray

Abstract


A graph H has a Gray code of k-colourings if it is possible to list all of its k-colourings in such a way that consecutive elements in the list differ in the colour of exactly one vertex. We prove that for any graph H, there is a least integer k0(H) such that H has a Gray code of k-colourings whenever kk0(H). We then determine k0(H) whenever H is a complete graph, tree, or cycle.

Keywords


graph colouring, cyclic Gray code

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DOI: https://doi.org/10.26493/1855-3974.196.0df

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications