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Graphs and Combinatorics

, Volume 32, Issue 5, pp 1945–1963 | Cite as

A Note on Non-reconstructible 3-Hypergraphs

  • William L. Kocay
Original Paper
  • 91 Downloads

Abstract

Non-reconstructible 3-hypergraphs are studied. A number of counting lemmas are proved for the subgraphs and sub-hypergraphs of a 3-hypergraph. A computer search is used to find all non-reconstructible 3-hypergraphs on at most 8 vertices and 11 triples. A characterization of pseudo-similar vertices in graphs is extended to 3-hypergraphs.

Keywords

Hypergraph Ulam’s problem Graph reconstruction  Subgraph counting Pseudo-similarity 

Mathematics Subject Classification

05C60 05C65 

Notes

Acknowledgments

Work on the computer program to count the number of 3-hypergraphs resulted from a discussion with Youssef Bouddabous while he was visiting the author.

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Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.Computer Science Department, St. Paul’s CollegeUniversity of ManitobaWinnipegCanada

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