4 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.

Reduced TAS-tree conjecture. For every undirected tree that is not a caterpillar, has at least $2$ vertices of even degree, and has no isomorphic pair, there exists some orientatio…

TAS-tree conjecture. For every undirected tree, there exists some orientation that has the tournament anti-Sidorenko property.