A note on the Caro-Tuza bound on the independence number of uniform hypergraphs

We show some consequences of Caro and Tuza’s [J. Graph Theory 15 (1991), 99–107] lower bound on the independence number of aK-uniform hypergraph H. This bound has the form CK · ∑n i=1(di+1) −1/(K−1), where CK is a constant depending only on K, and d1, . . . , dn are the degrees of the vertices in H. We improve on the best known bounds for CK : in particular, we prove that C3 ≥ √π/2 and that CK ≥ exp(−γ/(K − 1)) for K ≥ 3, where γ is the Euler-Mascheroni constant.