10 problems

A thrackle is a simple topological graph in which every pair of edges that do not share a vertex crosses. Conway's thrackle conjecture. Every thrackle with $n$ vertices has at most…

Let $\operatorname{tg}(G)$ denote the minimum genus of an orientable surface on which the graph $G$ can be thrackled. Linear thrackle-genus conjecture. … The source has already est…

Let $S_g$ be a compact orientable surface of genus $g>0$, and let $G$ be a graph with $n$ vertices and $m$ edges. Cairns–Nikolayevsky's conjecture. If $G$ can be thrackled on $S_g$…

Agoston et al.'s conjecture. A convex hull thrackle on $n$ points has at most $n$ convex hulls.

Let $G$ be an augmented caterpillar drawn as a great-circle thrackle, and let $v$ and $v'$ be adjacent vertices in the spine of $G$. A separating $2$-path at a vertex is a $2$-path…

A great-circle thrackleable tree is a tree admitting a thrackle drawing on the sphere in which the edges are great-circle arcs. An augmented caterpillar is the graph class defined…

A thrackle drawing is a drawing of a graph in which every pair of edges meets exactly once; a great-circle thrackle drawing is such a drawing on the sphere using great-circle arcs.…

Let $K_n$ be the complete graph on $n$ vertices, and let antithickness be the minimum number of thrackles in an edge-partition of a graph. Complete-graph antithickness conjecture.…

Let a $(d-1)$-thrackle be a higher-dimensional thrackle with $m$ facets and $n$ ridges. Continuous higher-dimensional thrackle conjecture. … This is proposed as the continuous anal…

Let $C_1,\dots,C_m\subseteq\mathbb{R}^2$ be convex polygons with a transversal set $W$ such that every pairwise intersection meets $W$ in exactly one point. Convex thrackle conject…