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

Xinmin Hou, Lei Yu, Jun Gao, Boyuan Liu

Published 2017-09-21Version 1

Determine the size of $r$-graphs with given graph parameters is an interesting problem. Chv\'atal 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.