The size of a graph is reconstructible from any n  2 cards
Brown, Paul and Fenner, Trevor (2017) The size of a graph is reconstructible from any n  2 cards. Discrete Mathematics 341 (1), pp. 165174. ISSN 0012365X.

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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 longstanding 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, vertexdeleted subgraphs, common cards, size reconstruction 
School:  School of Business, Economics & Informatics > Computer Science and Information Systems 
Depositing User:  Trevor Fenner 
Date Deposited:  22 Sep 2017 08:10 
Last Modified:  13 Feb 2021 03:29 
URI:  https://eprints.bbk.ac.uk/id/eprint/19609 
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