Size of a 3-uniform linear hypergraph

TL;DR

This paper establishes bounds on the size of 3-uniform linear hypergraphs based on their matching number and maximum degree, providing new theoretical limits for such structures.

Contribution

It introduces new bounds relating the size, maximum degree, and matching number of 3-uniform linear hypergraphs under specific conditions.

Findings

Bound: |F| ≤ Δν when Δ ≥ (23/6)ν(1+1/(ν-1))

Provides theoretical limits for hypergraph size based on degree and matching number

Enhances understanding of structural properties of 3-uniform linear hypergraphs

Abstract

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 $\mathcal{F}$ has maximum matching size $\nu$ and maximum degree $\Delta$ such that $\Delta\geq \frac{23}{6}\nu(1+\frac{1}{\nu-1})$, then $|\mathcal{F}|\leq \Delta \nu$.