DualHypergraph - Maple Help
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Hypergraphs

  

DualHypergraph

  

Return the dual of an hypergraph

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

DualHypergraph(H)

Parameters

H

-

Hypergraph

Description

• 

The command DualHypergraph(H) returns the dual hypergraph of H. ##

Terminology

• 

Dual hypergraph : If H :=(X, Y) is a hypergraph, then the dual hypergraph of H is the hypergraph whose vertex set is Y and where  {y1, y2, ...} is a hyperedge if y1, y2, ... intersect at a single vertex of H and {y1, y2, ...} is inclusion-maximal with that property.

• 

In broad terms, if H :=(X, Y) is a hypergraph without isolated vertices (that is, without vertices of degree zero) then the dual hypergraph of H is essentially (Y, X) and, thus, H  and the dual of its dual isomorphic.

Examples

Consider the Lovasz hypergraph of rank 3.

(1)

Draw a graphical representation of L3.

Compute the dual hypergraph DL3 of of L3.

(2)

Draw a graphical representation of DF4.

Check whether L3 and DL3 are isomorphic or not.

(3)

Check that L3 and the dual of DL3 are isomorphic.

(4)

Consider the Fan hypergraph of rank 4.

(5)

Draw a graphical representation of F4.

Compute the dual hypergraph DF4 of of F4.

(6)

Draw a graphical representation of DF4.

Check that F4 and DF4 are isomorphic.

(7)

References

  

Claude Berge. Hypergraphes. Combinatoires des ensembles finis. 1987,  Paris, Gauthier-Villars, translated to English.

  

Claude Berge. Hypergraphs. Combinatorics of Finite Sets.  1989, Amsterdam, North-Holland Mathematical Library, Elsevier, translated from French.

  

Charles Leiserson, Liyun Li, Marc Moreno Maza and Yuzhen Xie " Parallel computation of the minimal elements of a poset." Proceedings of the 4th International Workshop on Parallel Symbolic Computation (PASCO) 2010: 53-62, ACM.

Compatibility

• 

The Hypergraphs[DualHypergraph] command was introduced in Maple 2024.

• 

For more information on Maple 2024 changes, see Updates in Maple 2024.

See Also

Hypergraphs[Hyperedges]

Hypergraphs[Hypergraph]

Hypergraphs[Vertices]

Hypergraphs[AreIsomorphic]

 


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