Electronic Resource
Springer
Acta applicandae mathematicae
52 (1998), S. 209-222
ISSN:
1572-9036
Keywords:
line graph
;
line hypergraph
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The survey is devoted to line graphs and a new multivalued function $$\mathcal{L} $$ 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 $$\mathcal{L} $$ . 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 $$\mathcal{L} $$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1005963110362
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