✦ LIBER ✦

Interval hypergraphs and D-interval hypergraphs

✍ Scribed by John I. Moore Jr.

Publisher: Elsevier Science
Year: 1977
Tongue: English
Weight: 449 KB
Volume: 17
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(77)90148-0

No coin nor oath required. For personal study only.

✦ Synopsis

A hypcrgraph H = ( ~,; g) is called an inler,, d hypergraph if there exists a one-try-one functio,~ [ mapping the elements of V h:~ points on the real line such that for each edge E, there is an interval !, containing the images of all elements of E, but not the images of any elements not in E,. The difference hypergraph D(H) determined by H is formed bv adding t:~ ~ all nonempty sets of the form E, -E,. where E, and E, are edges of H H is said to be a D-interval hypergraph if D(H) is an interval hypergraph. A forbidden subhypergraph characterization of D-interval hypergraphs is given. By relating D-interval hypergraphs to dimension theory for posets, ~ve determine all 3-irreducible 7~osets of length one.

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