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    The size of a graph is reconstructible from any n - 2 cards

    Brown, Paul and Fenner, Trevor (2018) The size of a graph is reconstructible from any n - 2 cards. Discrete Mathematics 341 (1), pp. 165-174. ISSN 0012-365X.

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    Abstract

    Let G and H be graphs of order n. The number of common cards of G and H is the maximum number of disjoint pairs (v, w), where v and w are vertices of G and H, respectively, such that G - v = H - w. We prove that if the number of common cards of G and H is at least n - 2 then G and H must have the same number of edges, when n ≥ 29. This is the first improvement on the long-standing result of Myrvold that if G and H have at least n - 1 common cards then they have the same number of edges. It also improves on the result of Woodall that the numbers of edges of G and H differ by at most one when they have n - 2 common cards.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): Graph reconstruction, vertex-deleted subgraphs, common cards, size reconstruction
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Trevor Fenner
    Date Deposited: 22 Sep 2017 08:10
    Last Modified: 27 Jul 2019 06:16
    URI: http://eprints.bbk.ac.uk/id/eprint/19609

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