6 problems

Let $G$ be a graph with $n$ vertices and $e$ edges. Suppose that there are constants $A,\alpha>0$ such that every subgraph $H$ of $G$ satisfies … Here, $\operatorname{cr}(G)$ denot…

Fix an integer $\ell\geq 0$. Let $e_\ell(n)$ denote the maximum number of edges in a subgraph of $D_n$ with local crossing number $\ell$, and let $C_\ell$ be the coefficient define…

Let $D_n$ be the graph under consideration, let $e_\ell(n)$ denote the maximum number of edges in a subgraph of $D_n$ with local crossing number $\ell$, and call an edge crossing f…

Blažek–Koman conjecture. For any positive integers $k$ and $n$,

Archdeacon's generalized Harary–Hill conjecture. In any rotation of $K_n$, the number of induced nonplanar $K_4$'s is at least

Let $K_n$ be the complete graph on $n$ vertices, let $uk(Kn)$ denote its minimum number of crossings in a $k$-page book drawing, and let $Zk(n)$ denote the number of crossings in…