Note: Hypergraphs and the Clar problem in hexagonal systems

Authors:
Khaled Salem;HernáN Abeledo
Affiliations:
Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC 20052, USA;Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC 20052, USA
Venue:
Discrete Optimization
Year:
2006

Citing 3
Cited 0

Integer and combinatorial optimization

Integer and combinatorial optimization
The Clar covering polynomial of hexagonal systems I

Discrete Applied Mathematics
The Clar covering polynomial of hexagonal systems III

Discrete Mathematics - Special issue on Combinatorics and Application

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Abstract

We show that for a hypergraph H that is separable and has the Helly property, the perfect matchings of H are the strongly stable sets of the line graph of H. Also, we show that the hypergraph generated by a hexagonal system is separable and has the Helly property. Finally, we note that the Clar problem of a hexagonal system is a minimum cardinality perfect matching problem of the hypergraph generated by the hexagonal system. Hence, the Clar problem of a hexagonal system is a minimum cardinality strongly stable set problem in the line graph of the hypergraph generated by the hexagonal system.