A curve that can be traced out without removing a pencil from the
paper, and which ends where it starts, is called unicursal. It must
not retrace any part of itself but it can cross over itself. Such
curves are always traversable.
It is always possible to colour the
regions formed by a unicursal curve using two colours so that no
two regions have the same colour if they have the same boundary.
In other words, A network which you can travel round completely
without using the same path twice.
For instance, in the Konigsburg bridge problem, the network of roads
and bridges is not unicursal. If a network is unicursal it has to