BIROn - Birkbeck Institutional Research Online

    Graphs without proper subgraphs of minimum degree 3 and short cycles

    Narins, L. and Pokrovskiy, Alexey and Szabó, T. (2016) Graphs without proper subgraphs of minimum degree 3 and short cycles. Combinatorica 37 (3), pp. 495-519. ISSN 0209-9683.

    [img]
    Preview
    Text
    1408.5289.pdf - Author's Accepted Manuscript

    Download (252kB) | Preview

    Abstract

    We study graphs on n vertices which have 2n−2 edges and no proper induced subgraphs of minimum degree 3. Erdős, Faudree, Gyárfás, and Schelp conjectured that such graphs always have cycles of lengths 3,4,5,…,C(n) for some function C(n) tending to infinity. We disprove this conjecture, resolve a related problem about leaf-to-leaf path lengths in trees, and characterize graphs with n vertices and 2n−2 edges, containing no proper subgraph of minimum degree 3.

    Metadata

    Item Type: Article
    Additional Information: The final publication is available at Springer via the link above.
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 21 Jan 2019 11:20
    Last Modified: 26 Jul 2019 16:23
    URI: http://eprints.bbk.ac.uk/id/eprint/25892

    Statistics

    Downloads
    Activity Overview
    104Downloads
    52Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item