  In 1968, Gallai conjectured that the edges of any connected graph with $n$
vertices can be partitioned into $\lceil \frac{n}{2} \rceil$ paths. We show
that this conjecture is true for every planar graph. More precisely, we show
that every connected planar graph except $K_3$ and $K_5^-$ ($K_5$ minus one
edge) can be decomposed into $\lfloor \frac{n}{2} \rfloor$ paths.
