Séminaire ART
organisé par l'équipe Algèbre, représentations, topologie
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Maria Aksenovich
Ramsey numbers for odd cycles
14 avril 2026 - 14:00Salle de séminaires IRMA
For a graph $G$ and integer $k$, the Ramsey number $R(G; k)$ is the smallest integer $n$ such that any edge-coloring of a complete graph $K_n$ on $n$ vertices with $k$ colors results in a monochromatic copy of $G$. Determining Ramsey numbers even in the case of two colors has been a stubborn problem since its introduction in 1930. Except for finding the classical Ramsey number $R(t) = R(K_t;2)$ for cliques, one of the main open problems in the area is to determine multicolour Ramsey numbers for cycles. For positive integers $k$ and $\ell$, we show that $R(C_{2 \ell + 1}; k) \leq (4 \ell)^k \cdot k^{k/\ell}$, where $C_{2\ell +1}$ is a cycle of length $2\ell+1$. This is the first improvement for fixed $\ell$ and large $k$ since the bound $2\ell (k+2)!$ by Erd\H{o}s et al. from 1973. This is a joint work with Wouter Cames van Batenburg, Oliver Janzer, Lukas Michel, and Mathieu Rundstr\"{o}m. -
Francesco Sala
tba
19 mai 2026 - 14:00Salle de séminaires IRMA
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Chris Bowman
tba
26 mai 2026 - 14:00Salle de séminaires IRMA