On the size of -uniform linear hypergraphs

This article provides bounds on the size of a 3 -uniform linear hypergraph with restricted matching number and maximum degree. In particular, we show that if a 3 -uniform, linear family F has maximum matching size ν and maximum degree Δ such that Δ ≥ 23 6 ν ( 1 + 1 ν − 1 ) , then ∣ F ∣ ≤ Δ ν .