Note on isomorphic hypergraphs and some extensions of Whitney's theorem to families of sets

AbstractH. Whitney proved that, apart from a simple exeptional case, whenever the line graphs of two finite graphs are isomorphic then so are the graphs themselves. In this note (i) similar results are proved for finite hypergraphs, (ii) it is shown that certain extensions of Whitney's theorem to hypergraphs are false, (iii) a Whitney-type theorem is established for infinite hypergraphs