(Solved): Discrete structures - Planar graphs  Orienting planar graphs 5 An orientation of a graph \( G=( ...

Orienting planar graphs 5 An orientation of a graph \( G=(V, E) \) is any directed graph \( G^{\prime}=\left(V, E^{\prime}\right) \) arising by replacing each edg \( \{u, v\} \in E \) either by the directed edge \( (u, v) \) or by the directed edge \( (v, u) \). Prove by induction that for every planar graph there is an orientation such that each vertex has at most five outgoing edges.