7 problems

Belkhechine et al.'s $Q_n$ conjecture.

Let $Q_n$ be the tournament on $[n]=\{1,\ldots,n\}$ obtained from the natural transitive tournament by reversing precisely the consecutive pairs $12,23,\ldots,(n-1)n$. Equivalently…

Even inversion blow-up conjecture.

Direction-independence conjecture. For every oriented graphs $L$ and $R$,

Alon et al.'s dijoin existence conjecture. For all $l,r\in\mathbb{N}$ with $l\ge3$ or $r\ge3$, there exist oriented graphs $L$ and $R$ such that

Aubian et al.'s conjecture. For every integer $k\ge 3$, there exists a tournament $T_k$ with

Bang-Jensen et al.'s dijoin conjecture. For oriented graphs $L$ and $R$,