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 {{harv|Berge|1989}}.

==Line graphs of ''k''-uniform hypergraphs, ''k'' ≥ 3==

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| title = Edge intersection of linear 3-uniform hypergraphs

| journal = Discrete Mathematics

| volume = 309 | pages = 3500–3517 | year = 2009 | doi:=10.1016/j.disc.2007.12.082}}.

*{{citation

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*{{citation

| first = Vitaly I. | last = Voloshin

| title = "Introduction to Graph and Hypergraph Theory

| ___location = New York | publisher = Nova Science Publishers, Inc. | year = 2009

| id = {{MathSciNet | id = 2514872}}}}