Euler Paths
Posted to Poetry
by beatvibe on 2003-06-17 19:09:00
In solving the Seven Bridges problem, Euler proved (after distilling the problem to abstract terms and establishing his definitions) that "if a network has more than two odd vertices, it does not have an Euler path."
But Euler also proved the converse: "If a network has two or less odd vertices, it has at least one Euler path."
So, yes, in a network with one (and only one) odd vertex, it's not only possible to have an Euler path, it's actually guaranteed.
