Improved bound on vertex degree version of Erdős matching conjecture

For a (Figure presented.) -uniform hypergraph (Figure presented.), let (Figure presented.) denote the minimum vertex degree of (Figure presented.), and (Figure presented.) denote the size of the largest matching in (Figure presented.). In this paper, we show that for any (Figure presented.) and (Figure presented.), there exists an integer (Figure presented.) such that for positive integers (Figure presented.) and (Figure presented.), if (Figure presented.) is an (Figure presented.) -vertex (Figure presented.) -graph with (Figure presented.), then (Figure presented.). This improves upon earlier results of Bollobás, Daykin, and Erdős for the range (Figure presented.) and Huang and Zhao for the range (Figure presented.).