4 problems

Gago–Coroničová-Hurajová–Madaras conjecture. For every rational $\alpha$ in the interval

Vertex-cut obstruction. There are no graphs $H_1,\dots,H_n$ such that $G[H_1,\dots,H_n]$ is betweenness-uniform.

Coroničová Hurajová–Gago–Madaras conjecture. For any graph $G$ on a vertex set $\{v_1,\dots,v_n\}$ there exist graphs $H_1,\dots,H_n$ such that $G[H_1,\dots,H_n]$ is betweenness-un…

Let $H(u;n_0,n_1)$ be the rooted depth-$2$ bipartite tree with bipartition $(A_0,A_1)$, where $|A_i|=n_i$ for $i\in\{0,1\}$, the root $u\in A_0$ is adjacent to every vertex of…