The city of Koenigsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges
The problem was to find a walk through the city that would cross each bridge once and only once. The islands could not be reached by any route other than the bridges, and every bridge must have been crossed completely every time (one could not walk half way onto the bridge and then turn around and later cross the other half from the other side).
Euler proved that the problem has no solution.
Koenigsbergigraph graph object with vertex attributes
‘name’ and ‘Euler_letter’, the latter is the notation
from Eulers original paper; and edge attributes name (the name
of the bridge) and ‘Euler_letter’, again, Euler's notation
from his paper. This dataset is in the public domain.