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

TL;DR

This paper establishes a tight upper bound on the size of 3-uniform hypergraphs with specified matching number and codegree, extending previous work on graph size bounds under degree constraints.

Contribution

It introduces a new tight upper bound for 3-uniform hypergraphs with bounded codegree and matching number, filling a gap in hypergraph extremal theory.

Findings

Derived a tight upper bound for 3-graphs with given codegree and matching number

Extended classical results from graphs to 3-uniform hypergraphs

Provides a theoretical framework for size constraints in hypergraph design

Abstract

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.