The double reconstruction conjecture about finite colored hypergraphs
type: Item
instance of: scholarly article
title: The double reconstruction conjecture about finite colored hypergraphs
zbMATH Open document ID: 0698.05056
DOI: 10.1016/0095-8956(92)90066-7
author: Kosaburo Hashiguchi
published in: Journal of Combinatorial Theory. Series B
publication date: 1992-01-01T00:00:00Z
review text: One of the most famous open problems about simple graphs is the Ulam's Reconstruction Conjecture which asserts any two hypomorphic simple graphs of order greater than two are isomorphic. \textit{W. L. Kocay} [J. Comb. Theory, Ser. B 42, 46-63 (1987; Zbl 0578.05052)] presented an infinite family of pairs \((X_ n,Y_ n)\), \(n\geq 2\), of 3-hypergraphs which is a hypermorphic pair but not an isomorphic pair. This paper introduces a new reconstruction conjecture about colored hypergraphs called the Double Reconstruction Conjecture. It is shown among others that (1) the restricted version of this conjecture about simple graphs is equivalent to the Ulam's Conjecture, and (2) each pair, \((X_ n,Y_ n)\), \(n\geq 2\), above does not satisfy the condition in this conjecture.
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 4144030
zbMATH Keywords: Ulam's reconstruction conjecture
zbMATH Keywords: colored hypergraphs
MaRDI profile type: Publication
full work available at URL: 0095-8956(92)90066-7
OpenAlex ID: W1981867266
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description: scientific article; zbMATH DE number 4144030