3 problems

Direction-flip conjecture. For all $k\geq 3$, an oriented path with $k$ edges and one direction flip ($\rightarrow\dots \rightarrow \leftarrow\dots \leftarrow$) is TAS.

TAS ubiquity conjecture. A $(\frac 1 2 - o_n(1))$ fraction of all oriented paths of length $n$ are TAS.

Let $k\in\mathbb N$, and let $\delta^0(D)$ denote the minimum semidegree of an oriented graph $D$. Stein's conjecture. Every oriented graph with $\delta^0(D)>k/2$ contains every or…