# Binary set systems and totally balanced hypergraphs

Abstract : A hypergraph $H$ is {\it(i) Totally balanced} if it does not contain a special cycle, {\it(ii) Binary} if it is closed under intersection and every hyperedge has at most two predecessors (for inclusion order). We show in this paper that a hypergraph $H$ is totally balanced if and only if it can be embedded into a binary hypergraph $H'$; $H'$ is said to be a {\it binary extension} of $H$. We give an efficient algorithm which, given a totally balanced hypergraph $H$, produces a minimal binary extension $\widehat{H}$ of $H$; in addition, if $H$ is a hierarchy or an interval hypergraph, then so is $\widehat{H}$.
Keywords :
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-02436247
Contributor : Pascal Préa <>
Submitted on : Thursday, February 25, 2021 - 12:33:58 PM
Last modification on : Friday, March 5, 2021 - 3:28:41 AM

### File

binary_hypergraphs.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-02436247, version 2

### Citation

Célia Châtel, François Brucker, Pascal Préa. Binary set systems and totally balanced hypergraphs. Discrete Applied Mathematics, Elsevier, In press. ⟨hal-02436247v2⟩

Record views