# The one-way street theorem

Robbins's theorem, also known as the one-way street theorem. This 1939 result of Herbert Robbins completely characterizes the undirected graphs that may be made into strongly connected graphs by orienting their edges: they are exactly the connected graphs that don't have any bridges.

Less abstractly, it's possible to make the street system of a city one-way (without causing some people to get stuck in dead ends) exactly when there is no possible road closure that would split the city into two disconnected parts.

A strongly connected orientation of a given bridgeless graph is easy to find: just perform a depth first search, orient the DFS tree edges away from the tree root, and orient the remaining edges towards the root.