| Title: | Weak k-reconstruction of Cartesian products graphs |
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| Authors: | ID Imrich, Wilfried (Author)
ID Zmazek, Blaž (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  http://dx.doi.org/10.1016/S1571-0653(04)00414-7
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.12 - Published Scientific Conference Contribution Abstract |
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| Organization: | PEF - Faculty of Education
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| 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 works of the authors and Sims. This paper also contains a counterexample to a conjecture of MacAvaney. |
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| Keywords: | matematika, teorija grafov, kartezični produkt, problem rekonstrukcije, sestavljeni grafi, mathematics, graph theory, reconstruction problem, Cartesian product, composite graphs |
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| Year of publishing: | 2001 |
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| Number of pages: | str. 1-4 |
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| Numbering: | Vol. 10 |
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| PID: | 20.500.12556/DKUM-51508  |
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| UDC: | 519.17 |
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| ISSN on article: | 1571-0653 |
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| COBISS.SI-ID: | 13824601 |
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| NUK URN: | URN:SI:UM:DK:WBTNPHIP |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1446 |
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| Downloads: | 21 |
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| Metadata: |    |
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| Categories: | Misc.
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