On intersection multigraphs of hypergraphs

AbstractThe sum of the cardinalities of all the edges of a hypergraph is computed in two different ways. This result is used to treat the generalisation of the notion of cyclomatic number for hypergraphs. Among others the following result is obtained: The cyclomatic number of the hypergraph H vanishes if and only if some maximum forest of the weighted intersection graph of H has the property that for every vertex of H the subgraph of the forest induced by those edges containing that vertex is connected