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    Partitioning edge-coloured complete graphs into monochromatic cycles and paths

    Pokrovskiy, Alexey (2014) Partitioning edge-coloured complete graphs into monochromatic cycles and paths. Journal of Combinatorial Theory, Series B 106 , pp. 70-97. ISSN 0095-8956.

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    Abstract

    A conjecture of Erdős, Gyárfás, and Pyber says that in any edge-colouring of a complete graph with r colours, it is possible to cover all the vertices with r vertex-disjoint monochromatic cycles. So far, this conjecture has been proven only for r = 2. In this paper we show that in fact this conjecture is false for all r > 2. In contrast to this, we show that in any edge-colouring of a complete graph with three colours, it is possible to cover all the vertices with three vertex-disjoint monochromatic paths, proving a particular case of a conjecture due to Gyárfás. As an intermediate result we show that in any edge-colouring of the complete graph with the colours red and blue, it is possible to cover all the vertices with a red path, and a disjoint blue balanced complete bipartite graph.

    Metadata

    Item Type: Article
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Research Centre: Applied Macroeconomics, Birkbeck Centre for
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 12 Dec 2018 16:46
    Last Modified: 12 Dec 2018 16:46
    URI: http://eprints.bbk.ac.uk/id/eprint/24978

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