Improved bound on vertex degree version of Erdős matching conjecture

Abstract

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