Hypergraphs and Whitney's theorem on edge-isomorphisms of graphs
type: Item
instance of: scholarly article
title: Hypergraphs and Whitney's theorem on edge-isomorphisms of graphs
zbMATH Open document ID: 0548.05046
DOI: 10.1016/0012-365X(84)90018-9
author: M. L. Gardner
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The s-line graph \(L_ s\) of a hypergraph \(H=(V,E)\) has E as its vertex- set and \(e_ 1\), \(e_ 2\) are adjacent in \(L_ s\) if \(| e_ 1\cap e_ 2|\geq s.\) First, operations are defined which permit to construct all the hypergraphs with a given 1-line graph starting from the dual hypergraph of this graph. From this: A triangle-free graph is the 1- line graph of a unique hypergraph. As a corollary Whitney's classical theorem on edge isomorphisms of graphs is obtained. A generalization of Whitney's theorem is proved: The strong isomorphisms of two hypergraphs of rank r follows under an additional condition if all corresponding pairs of partial hypergraphs on \(\lceil\log_ 2r\rceil\) of the edges are strongly isomorphic. This implies several corollaries.
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 3873375
zbMATH Keywords: line graph
zbMATH Keywords: edge isomorphism
zbMATH Keywords: strong isomorphism
MaRDI profile type: Publication
cites work: Q3941433
cites work: Note on isomorphic hypergraphs and some extensions of Whitney's theorem to families of sets
cites work: Q4200103
cites work: Parallel concepts in graph theory
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description: scientific article; zbMATH DE number 3873375