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ArticleOriginal scientific text

Title

Weak k-reconstruction of Cartesian products

Authors 1, 2, 3, 2, 3

Affiliations

  1. Montanuniversität Leoben, Institut für Mathematik und Angewandte Geometrie, Franz-Josef Straße 18, A-8700 Leoben, Austria
  2. University of Maribor, Faculty of Mechanical Engineering, Smetanova 17, 2000 Maribor, Slovenia
  3. IMFM, Jadranska 19, Ljubljana

Abstract

By Ulam's conjecture every finite graph G can be reconstructed from its deck of vertex deleted subgraphs. The conjecture is still open, but many special cases have been settled. In particular, one can reconstruct Cartesian products. We consider the case of k-vertex deleted subgraphs of Cartesian products, and prove that one can decide whether a graph H is a k-vertex deleted subgraph of a Cartesian product G with at least k+1 prime factors on at least k+1 vertices each, and that H uniquely determines G. This extends previous work of the authors and Sims. The paper also contains a counterexample to a conjecture of MacAvaney.

Keywords

ENG
reconstruction problem, Cartesian product, composite graphs

Bibliography

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Discussiones Mathematicae Graph Theory
2003/23/2
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Pages:
273-285
Main language of publication
English
Received
2001-09-26
Accepted
2002-04-12
Published
2003

DOI: 10.7151/dmgt.1202

Exact and natural sciences