An upper bound on the path number of a digraph

A proof is presented of the conjecture of Alspach and Pullman that for any digraph G on n ≥ 4 vertices, the path number of G is at most [n24].

[1]  Brian Alspach,et al.  Path numbers of tournaments , 1976 .

[2]  Brian Alspach,et al.  Path decompositions of digraphs , 1974, Bulletin of the Australian Mathematical Society.