Abstract: Given a hypergraph H(V, E), a set of vertices S ⊆ V is a vertex cover if every edge has at least one vertex in S. The vertex cover number is the minimum cardinality of a vertex cover, denoted by τ(H). In this paper, we prove that for every 3-uniform connected hypergraphH(V, E), τ(H) ≤ 2m/3+1 holds on where m is the number of edges. Furthermore, the equality holds on if and only if H(V, E) is a hypertree with perfect matching.

Key words: 3-Uniform hypergraph, Vertex cover, Hypertree, Perfect matching