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    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.

    1408.5289.pdf - Author's Accepted Manuscript

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    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.


    Item Type: Article
    Additional Information: The final publication is available at Springer via the link above.
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 21 Jan 2019 11:20
    Last Modified: 02 Aug 2023 17:47


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