Independence in uniform linear triangle-free hypergraphs

The independence number α(H)α(H) of a hypergraph HH is the maximum cardinality of a set of vertices of HH that does not contain an edge of HH. Generalizing Shearer’s classical lower bound on the independence number of triangle-free graphs Shearer (1991), and considerably improving recent results of Li and Zang (2006) and Chishti et al. (2014), we show that α(H)≥∑u∈V(H)fr(dH(u)) for an rr-uniform linear triangle-free hypergraph HH with r≥2r≥2, where fr(0)=1,andfr(d)=1+((r−1)d2−d)fr(d−1)1+(r−1)d2for  d≥1.