In 1976, Alspach, Mason, and Pullman conjectured that any tournament T of even order can be decomposed into exactly \(\mathrm{ex}(T)\) paths, where \(\mathrm{ex}(T) = \frac{1}{2}\sum _{v\in V(T)}|d_T^+(v)-d_T^-(v)|\). We prove this conjecture for all sufficiently large tournaments. We also prove an asymptotically optimal result for tournaments of odd order.
