Line Hypergraphs: A Survey

The survey is devoted to line graphs and a new multivalued function 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 . There are many publications about line graphs, but our considerations are restricted to papers concerning Krausz global characterization of line graphs or Whitneys theorem on edge isomorphisms. The survey covers almost all known results on the function because they are concentrated around Krausz and Whitneys 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.