Author

M. Axenovich

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Preprint Aug 2026

On high-girth layered graphs of positive Tur\'an density in a hypercube

For a graph $H$, let $\operatorname{ex}(Q_n, H)$ be the largest number of edges in a subgraph of the hypercube $Q_n$ of dimension $n$ that contains no subgraph isomorphic to $H$. The Tur\'an density of $H$ in a hypercube, denoted $\pi_\square(H)$, is defined as $\lim_{n\rightarrow \infty} \operatorname{ex}(Q_n, H)/|E(Q...

M. Axenovich, Marko Pejić · 0 citations

Preprint Aug 2026

Vertex-Ramsey theorems for Cartesian powers of graphs

For graphs $G,H$ and positive integers $r$ and $n$ we write $G^{\square n} \xrightarrow{r} H$ if every $r$-vertex-coloring of the Cartesian power $G^{\square n}$ of $G$ contains a monochromatic copy of $H$. Since chromatic number $\chi$ of $G^{\square n}$ is the same as $\chi(G)$, there is an $r$-vertex coloring of $G^...

N'ora Alm'asi, M. Axenovich, Arsenii Sagdeev · 1 citation