Observing somebody crossing the river with a graph of children,
we could make a sequence of snapshots in order to be able to remember what was done in what order.
The crucial snapshots we call states.
Snapshots where the boat is on its way on the river are not too interesting,
whence we concentrate on cases where the boat lies on a bank.
Since loading and unloading goes very easily and quickly,
we may assume that always all children are first unloaded,
before new children---possibly among them some who were on the boat already---
board.
Thus
states are situations where the boat lies on either the left or the right bank.
Below is a right-bank state and a left-state bank for the game graph seen to the right.
Of course, since presently there is no fight on the non-boat bank,
the vertices on this other bank must be independent then.
We can also refer to states by highlighting the independent set
of vertices on the other bank in yellow or green, depending whether
it is a left- or right-bank state.
