(and Hamiltonian circuit)
by Christy Bergman,
Paris, France 2005.
Note: This poem came after re-reading my journal from my trip to Morocco. I used the writer's technique called "clustering" (free-associating words around a central subject to get down quickly all the first thoughts and then drawing lines between associations). Then I turned this "cluster" into a network and found a Hamiltonian circuit (traveling salesman solution) through it. That is, a path through the network that visits each vertex only once, except possibly the starting/ending vertex which could be the same. This circuit determines the order for the stanzas, where each stanza is about the key word which is currently being visited.
Hamiltonian circuits were made famous in 1857 by a game called "Around the World", but were first discovered by Leonard Euler (1707-1783). Euler was inspired by a real world problem in his home town Köningsberg in which runs the Pregel river. The residents of the town debated whether it was possible to walk from any point in the town, cross over each of the 7 bridges which connected two islands and the mainland without crossing over any bridge twice. Euler took the problem and generalized the town map to a network or graph. Then he proved that such a path through a network does not exist if there are more than two vertices with an odd number of paths converging to them. That is, the Eulerian path cannot be found through networks with more than two odd vertices. Incidentally, the Köningsberg network did not have an Eulerian path through it.