§ DFS numbers as a monotone map
Really, we want a partial order that is defined with the tree as the
Hasse diagram. However, performing operations on this is hard. Hence,
the DFS numbering is a good monotone map from this partial order
to the naturals, which creates a total order.
I want to think about this deeper, I feel that this might be a good way
to think about the
low numbers that show up in
tarjan's algorithm for strongly connected components
This also begs the question: can we use other partial orders, that chunk
some information, but don't lose all the information as going to a total
order (the naturals) does?