ComplementHypergraph - Maple Help
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Hypergraphs

  

ComplementHypergraph

  

Return the complement of an hypergraph

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

ComplementHypergraph(H)

Parameters

H

-

Hypergraph

Description

• 

The command ComplementHypergraph(H) returns the complement hypergraph of H.

Terminology

• 

Complement hypergraph :  If H :=(X, Y) is a hypergraph, then the complement hypergraph of H is the hypergraph (X, Z) where Z is the set of the complements in X of the hyperedges of H.

Examples

Consider the Fan hypergraph of rank 4.

(1)

Draw a graphical representation of F4.

Compute the complement hypergraph C of of F4.

(2)

Draw a graphical representation of C.

Consider these two Kuratowski hypergraphs.

(3)

Draw a graphical representation of K2.

Draw a graphical representation of K3.

Observe that K3 is the complement hypergraph of K2.

(4)

Observe that K2 is the complement hypergraph of K3.

(5)

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[ComplementHypergraph] 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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