A Systematic Research on Various Types of Hausdorff Hypergraphs

A hypergraph H = (V, E) is said to be a Hausdorff hypergraph if for any two distinct vertices u, v of V there exist hyperedges e1, e2 ∈ E such that u ∈ e1, v ∈ e2 and e1 ∩ e2 = ∅. In this paper we have discussed hausdorff property of hypergraphs as well as minimal hausdorff hypergraph. Previous work on Hausdorff-type separation properties, driven by classical topology and graph theory, has included the study of specific types of hypergraphs to address vertex separability with disjoint hyperedges. Continuing from this stream of research, this work aims to conduct an in-depth study of Hausdorff hypergraphs, with special emphasis on minimal Hausdorff hypergraphs and their variants. We obtain results on minimal Hausdorff hypergraphs with respect to bounds of the number of hyperedges and study sufficient conditions for competition hypergraphs of digraphs and independent hypergraphs of graphs to be Hausdorff. Links with conformal hypergraphs, cyclomatic number, and acyclicity are considered in an attempt to cover