Sufficient Conditions for Spanning k ‐Hypertrees via Distance Spectral Radius of Hypergraphs

For an integer k ≥ 2, a spanning k ‐hypertree T is defined as a spanning hypertree ( β ‐acyclic) such that the maximum degree d T ( v ) of every vertex v ∈ V ( T ) is at most k . A sufficient condition for the existence of a spanning k ‐hypertree in connected hypergraphs is established. The algorithm for checking the existence of a spanning k ‐hypertree and its complexity analysis are also presented. The distance spectral radius of a hypergraph H , denoted as λ ( D ( H )), is defined as the largest eigenvalue of its distance matrix D ( H ). A lower bound for λ ( D ( H )) is established for a connected hypergraph H . Combined with typical distance spectral techniques and structural analysis of hypergraphs, this bound yields sufficient conditions for the existence of spanning k ‐hypertrees in terms of the distance spectral radius.