11 problems

Let $H$ be a graph, and let $G$ be an $n$-vertex graph satisfying the minimum-degree condition in Komlós's almost-perfect tiling theorem, namely $\delta(G)\geq (1-1/\chi_{cr}(H))n$…

Treglown's conjecture. There exists $n_0$ such that, for every $n\in 3\mathbb{Z}$ with $n\geq n_0$, every oriented graph $G$ on $n$ vertices satisfying

Let $H$ be a graph, let $h=|V(H)|$, and let $G$ be an $n$-vertex graph. In the Alon–Yuster almost-factor and factor results, the error terms of order $\varepsilon n$ are additive c…

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…

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 graph that is not a disjoint union of isolated vertices, and let $\delta_{sub}(n,H)$ denote the minimum degree threshold ensuring a perfect $H$-subdivision tiling in e…

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…

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…

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…

Let $G$ be a digraph on $n$ vertices, where $3$ divides $n$. A digraph is strongly $2$-connected if it remains strongly connected after the deletion of any one vertex. Molla's conj…