Eero Räty

most citedPositive discrepancy, MaxCut, and eigenvalues of graphs

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math.CO2023★ 1 cited

Positive discrepancy, MaxCut, and eigenvalues of graphs

Eero Räty, Benny Sudakov, István Tomon

The positive discrepancy of a graph $G$ of edge density $p = e (G) / (2 v ( G ))$ is defined as $$\mbox{disc}^{+}(G)=\max_{U\subset V(G)}e(G[U])-p\binom{|U|}{2}.$$ In 1993, Alon pro…

math.CO2023

Dedekind's problem in the hypergrid

Victor Falgas-Ravry, Eero Räty, István Tomon

Consider the partially ordered set on $[t]^{n} := {0, \dots, t - 1}^{n}$ equipped with the natural coordinate-wise ordering. Let $A (t, n)$ denote the number of antichains of this poset. The…

math.CO2023

Minimum degree conditions for rainbow triangles

Victor Falgas-Ravry, Klas Markström, Eero Räty

Let $G := (G_{1}, G_{2}, G_{3})$ be a triple of graphs on a common 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\…

math.CO2023

Exponential Erdős-Szekeres theorem for matrices

Recep Altar Çiçeksiz, Zhihan Jin, Eero Räty +1

In 1993, Fishburn and Graham established the following qualitative extension of the classical Erdős-Szekeres theorem. If $N$ is sufficiently large with respect to $n$ , then any $N\…