Why connectedness is hard to compute
Even for simple line drawings, there are
exponentially many cases.
Removing one segment can break
connectedness
But this depends on the precise
arrangement of the other pieces.
Unlike parity, there are no simple
summaries of the other pieces that tell
us what will happen.
Connectedness is easy to compute with an
iterative algorithm.
Start anywhere in the ink
Propagate a marker
See if all the ink gets marked.