BIROn - Birkbeck Institutional Research Online

    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.

    [img]
    Preview
    Text
    1205.5492.pdf - Draft Version

    Download (550kB) | Preview

    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 Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Research Centres and Institutes: Applied Macroeconomics, Birkbeck Centre for
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 12 Dec 2018 16:46
    Last Modified: 06 Aug 2024 20:22
    URI: https://eprints.bbk.ac.uk/id/eprint/24978

    Statistics

    Activity Overview
    6 month trend
    287Downloads
    6 month trend
    177Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item
    Edit/View Item