Spanning Hypertrees and Spanning Superhypertrees

Graph theory provides a rigorous foundation for representing relationships and connectivity through vertices and edges. Hypergraphs extend this framework by introducing hyperedges that connect more than two vertices. Superhypergraphs further enhance the model via iterated powerset constructions, capturing hierarchical and self-referential structures among hyperedges. A spanning tree is a connected, acyclic subgraph that covers all vertices of a graph with exactly |V| − 1 edges. A spanning hypertree is a connected, Berge-acyclic subhypergraph of a uniform hypergraph that spans all vertices with hypertree structure. In this paper, we study the notion of a spanning superhypertree as the natural spanning tree concept within superhypergraphs. We also discuss several concrete realworld examples of spanning superhypertrees and analyze their structural properties.