Eero Räty

collaborators

3 papers

math.CO2024

Large Cuts in Hypergraphs via Energy

Eero RÃ¤ty, IstvÃ¡n Tomon

A simple probabilistic argument shows that every $r$ -uniform hypergraph with $m$ edges contains an $r$ -partite subhypergraph with at least $\frac{r !}{r ^{r}} m$ edges. The celebrated r…

math.CO2024

Bisection Width, Discrepancy, and Eigenvalues of Hypergraphs

Eero RÃ¤ty, IstvÃ¡n Tomon

A celebrated result of Alon from 1993 states that any $d$ -regular graph on $n$ vertices (where $d = O (n^{1/9})$ ) has a bisection with at most $\frac{dn}{2}(\frac{1}{2}-Î©(\frac{1}{\s…

math.CO2024

Rainbow variations on a theme by Mantel: extremal problems for Gallai colouring templates

Victor Falgas-Ravry, Klas MarkstrÃ¶m, Eero RÃ¤ty

Let $G := (G_{1}, G_{2}, G_{3})$ be a triple of graphs on the same vertex set $V$ of size $n$ . A rainbow triangle in $G$ is a triple of edges $(e_{1}, e_{2}, e_{3})$ with $e_i\…