Erd\H{o}s et al. (JCT-B, 1989) conjectured that, for integers $r\ge 2$ and $\delta\ge 2$ with $3r-1\mid\delta$, every connected $K_{2r+1}$-free graph of order $n$ and minimum degree $\delta$ has diameter at most $ \frac{3r-1}{r}\cdot \frac{n}{\delta}+O(1)$. Czabarka et al. (JCT-B, 2021) later proposed the following gen...
Let $f(k)$ denote the smallest integer such that every oriented graph $D$ with chromatic number at least $f(k)$ contains every oriented tree on $k$ vertices. Burr (1980) showed that $f(k)\le (k-1)^2$ and conjectured that $f(k)=2k-2$. Bessy, Gon\c{c}alves and Reinald (2025) proved that $f(k)=O(k^{3/2})$. In this paper,...
The \emph{$k$-color Ramsey number} $R_k(C_{2\ell+1})$ is the least integer $n$ such that any $k$-edge-coloring of a complete graph $K_n$ has a monochromatic odd cycle $C_{2\ell+1}$. Axenovich, Cames van Batenburg, Janzer, Michel, and Rundstr\"om~(JCT-B, 2026) recently proved \[ R_k(C_{2\ell+1})\le (4\ell-2)^k k^{k/\ell...
