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- Title
Degree Lists and Connectedness are 3-Reconstructible for Graphs with At Least Seven Vertices.
- Authors
Kostochka, Alexandr V.; Nahvi, Mina; West, Douglas B.; Zirlin, Dara
- Abstract
The k-deck of a graph is the multiset of its subgraphs induced by k vertices. A graph or graph property is l-reconstructible if it is determined by the deck of subgraphs obtained by deleting l vertices. We show that the degree list of an n-vertex graph is 3-reconstructible when n ≥ 7 , and the threshold on n is sharp. Using this result, we show that when n ≥ 7 the (n - 3) -deck also determines whether an n-vertex graph is connected; this is also sharp. These results extend the results of Chernyak and Manvel, respectively, that the degree list and connectedness are 2-reconstructible when n ≥ 6 , which are also sharp.
- Subjects
SUBGRAPHS; MATHEMATICAL connectedness; FUZZY graphs
- Publication
Graphs & Combinatorics, 2020, Vol 36, Issue 3, p491
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-020-02131-6