Irregularity Strength of Uniform Hypergraphs

Abstract

A hypergraph is irregular if no two of its vertices have the same degree. It is shown that for all $r\ge 3$ and $n\ge r+3$, there exist irregular $r$-uniform hypergraphs of order $n$. For $r\ge 6$ it is proved that almost all $r$-uniform hypergraphs are irregular. A linear upper bound is given for the irregularity strength of hypergraphs of order $n$ and fixed rank. Furthermore, the irregularity strength of complete and complete equipartite hypergraphs is determined.