Partial Total Domination in Hypergraphs

This paper establishes fundamental results for partial total domination in hypergraphs. We present tight bounds for the partial total domination number in k-uniform hypergraphs, demonstrate relationships with classical domination parameters, and provide constructive proofs using hypergraph transformation techniques. Applications in sensor networks and biological systems are discussed with supporting examples. Key results include a general upper bound of kk−1γ(H) for k-uniform hypergraphs without isolated vertices, verified through both analytic methods and computational examples.