Co-degree density of hypergraphs

For an r-graph H, let C(H)=minSd(S), where the minimum is taken over all (r−1)-sets of vertices of H, and d(S) is the number of vertices v such that S∪{v} is an edge of H. Given a family F of r-graphs, the co-degree Turán number is the maximum of C(H) among all r-graphs H which contain no member of F as a subhypergraph. Define the co-degree density of a family F to be

     

The size of 3-uniform hypergraphs with given matching number and codegree

To determine the size of $r$-graphs with given graph parameters is an interesting problem. Chvátal and Hanson (JCTB, 1976) gave a tight upper bound of the size of 2-graphs with restricted maximum degree and matching number; Khare (DM, 2014) studied the same problem for linear 3-graphs with restricted matching number and maximum degree. In this paper, we give a tight upper bound of the size of 3-graphs with bounded codegree and matching number.