Hypergraphs and the Clar problem in hexagonal systems

We show that for a hypergraph HH that is separable and has the Helly property, the perfect matchings of HH are the strongly stable sets of the line graph of HH. 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.