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Line hypergraphs: A survey

Tyshkevich, Regina; Zverovich, Vadim

Authors

Regina Tyshkevich



Abstract

The survey is devoted to line graphs and a new multivalued function L called the line hypergraph. This function generalizes two classical concepts at once, namely the line graph and the dual hypergraph. In a certain sense, line graphs and dual hypergraphs are extreme values of the function L. There are many publications about line graphs, but our considerations are restricted to papers concerning Krausz’ global characterization of line graphs or Whitney’s theorem on edge isomorphisms. The survey covers almost all known results on the function L because they are concentrated around Krausz’ and Whitney’s theorems. These results provide evidence that the notion of the line hypergraph is quite natural. It enables one to unify the classical theorems on line graphs and to obtain their more general versions in a simpler way.

Citation

Tyshkevich, R., & Zverovich, V. (1998). Line hypergraphs: A survey. Acta Applicandae Mathematicae, 52(1), 209-222. https://doi.org/10.1023/A%3A1005963110362

Journal Article Type Article
Publication Date Jul 1, 1998
Journal Acta Applicandae Mathematicae
Print ISSN 0167-8019
Publisher Springer (part of Springer Nature)
Peer Reviewed Peer Reviewed
Volume 52
Issue 1
Pages 209-222
DOI https://doi.org/10.1023/A%3A1005963110362
Keywords line graph, line hypergraph
Public URL https://uwe-repository.worktribe.com/output/1099669
Publisher URL http://dx.doi.org/10.1023/A:1005963110362