The Königsberg Bridge Problem Revisited – Eulerian Paths

Euler’s solution to the Seven Bridges gave birth to graph theory. Today, we use Eulerian paths to design snowplow routes (covering every road once), DNA fragment assembly (finding a path through overlap graph), and the Chinese Postman Problem. The condition remains: a graph has an Eulerian circuit (returns to start) iff all vertices have even degree. The handshaking lemma (sum of degrees = 2×edges) is a direct consequence. Euler’s insight shows that the shape of a network matters more than distances.