The acyclic-orientations tag has no usage guidance.

**5**

votes

**1**answer

132 views

### When can we make a digraph acyclic by fliping groups of arcs?

We have a digraph D=(V,A) and its arc set A is partitioned into classes. We can flip the classes, which means changing the direction of all the arcs in the class.
Is there any result on when can we ...

**3**

votes

**1**answer

429 views

### Acyclic orientations of complete graphs in terms of Stirling numbers?

It is well-known that the number of acyclic orientations of $K_n$ is $n!$. Does anybody know of a combinatorial argument for this fact which uses the identity:
$$n!=\sum_{k=1}^ns(n,k),$$
where the ...