Bridge walk · currently at A

Eulerian: no

Walk

0 / 7 bridges crossed

Parity

4 odd-degree vertices

Legend

Click an amber bridge from your current vertex. Greyed dashed bridges are inactive.

The Königsberg Bridges

Seven bridges, one impossible walk

In 1736 Leonhard Euler proved that there is no way to cross all seven bridges of Königsberg exactly once. The proof: reduce the map to a graph; an Eulerian path exists only if at most two land masses have an odd number of bridges. Königsberg had four with odd degree. With that argument Euler invented graph theory.

Start at

Currently at: A

Vertex degrees

odd

Eulerian path ⇔ at most two vertices have odd degree (and the graph is connected).

Bridges

The seven historical bridges are on by default. Toggle them to see how the parity argument shifts. The Honey Bridge (BC) was built later — adding it changes everything.

Königsberg's seven bridges have no Eulerian path. Click to watch a greedy walk from the start and see it get stuck — that's the whole point of Euler's argument.

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