On neighbourhood line graphs
type: Item
instance of: scholarly article
title: On neighbourhood line graphs
zbMATH Open document ID: 0747.05096
DOI: 10.1016/0012-365X(90)90238-D
author: Xingxing Yu
published in: Discrete Mathematics
publication date: 1992-06-28T00:00:00Z
review text: First the author shows that the answers to two questions due to A. Neumaier are `No'. Then he shows how to modifiy the second question in order to obtain an affirmative answer. In fact he proves (in design theoretical terminology) the following: Let \(G\) be some (connected) graph where each neighborhood induces a line graph and where each edge is contained in some triangle. Then \(G\) is the underlying graph of some (connected) hypergraph (i.e. set system) where any two distinct vertices lie in 0 or 2 common hyperedges and any two distinct hyperedges contain at most 2 common vertices.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 32369
zbMATH Keywords: line graphs
zbMATH Keywords: hypergraphs
zbMATH Keywords: designs
reviewed by: Erich Prisner
MaRDI profile type: Publication
cites work: Line graphs, root systems, and elliptic geometry
cites work: Q3872508
cites work: On designs
full work available at URL: 0012-365x(90)90238-d
OpenAlex ID: W2083628949
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description: scientific article; zbMATH DE number 32369