6 problems

Let $H$ be an ordered graph. An $H$-tiling in an ordered graph $G$ is a collection of vertex-disjoint copies of $H$ in $G$, and let $\delta(G)$ denote the minimum degree of $G$. Wr…

Grinshpun–Sárközy conjecture. For every positive integer $r$ there exists a constant $C_r$ such that, for every $\Delta\geq 2$ and every $\Delta$-bounded graph sequence…

Let $k\geq r\geq 2$ and $\gamma>0$. Let $G$ be a $k$-partite graph on $n$ vertices with parts $V_1,\ldots,V_k$ such that $|V_i|\leq n/r$ for every $i$. For each $i\in [k]$, write…

Let $r$ and $k$ be integers satisfying $1\le r\le k$ and $k\ge 3$. The Ramsey–Turán tiling function ${\bf{RTT}}_r(K_k)$ is defined as the asymptotic minimum-degree threshold for fo…

Balogh, Kostochka and Treglown's conjecture. Then $G$ contains a perfect $K_r$-tiling, that is, a collection of vertex-disjoint copies of $K_r$ covering all vertices of $G$.

Let $H$ be a non-empty subgraph of the hypercube $Q_k$ for some $k$. Leader–Tan edge-decomposition conjecture. There exists a positive integer $n$ such that the edges of $Q_n$ can…