Brown, Paul and Fenner, Trevor (2017) 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 Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Trevor Fenner |
| Date Deposited: | 22 Sep 2017 08:10 |
| Last Modified: | 09 Aug 2023 12:42 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/19609 |
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