On the Matching Number of k-Uniform Connected Hypergraphs with Maximum Degree.

For k ≥ 2 , let H ( V , E ) be a k -uniform connected hypergraph with maximum degree Δ on n vertices and m edges. A set of edges A ⊆ E is a matching if every two distinct edges in A have no common vertices. The matching number is the maximum cardinality of a matching, denoted by ν ( H ) . In this paper, we prove the following inequality: ν ( H ) ≥ n - ( k - 2 ) m - 1 Δ and characterize the extremal hypergraphs with equality holds. A class of hypergraphs called Δ -star hypertrees are introduced, which are exactly the extremal hypergraphs. These results is a generalization of the theorems by Tang and Diao in IJTCS-FAW 2022.