Line graph of a hypergraph: Difference between revisions

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Questions about line graphs of hypergraphs are often generalizations of questions about line graphs of graphs. For instance, a hypergraph whose edges all have size ''k'' is called ''k'''''-uniform'''. (A 2-uniform hypergraph is a graph). In hypergraph theory, it is often natural to require that hypergraphs be ''k''-uniform. Every graph is the line graph of some hypergraph, but, given a fixed edge size ''k'', not every graph is a line graph of some ''k''-uniform hypergraph. A main problem is to characterize those that are, for each ''k'' ≥ 3.

A hypergraph is '''linear''' if each pair of hyperedges intersects in at most one vertex. Every graph is the line graph, not only of some hypergraph, but of some linear hypergraph.<ref> {{Cite bookharv|last=Berge, C. (Claude)|first=|url=http://worldcat.org/oclc/898849714|title=Hypergraphs : combinatorics of finite sets|date=1989|publisher=North Holland|others=MR 1013569|year=|isbn=0-444-87489-5|___location=|pages=|language=Translated from the French.|oclc=898849714}}</ref>.

==Line graphs of ''k''-uniform hypergraphs, ''k'' &ge; 3==

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| editor3-first = H. | editor3-last = Walther

| publisher = Teubner | ___location = Leipzig | pages = 17–23 | year = 1968}}.

*{{citation|last=Berge|first=C.|title=Hypergraphs: Combinatorics of Finite Sets|year=1989|___location=Amsterdam|publisher=North-Holland|mr=1013569|authorlink=Claude Berge}}. Translated from the French.

*{{citation