Minimum path decompositions of oriented cubic graphs
K. B. Reid, Keith Wayland · Journal of Graph Theory · 1987
Abstract Pullman [3] conjectured that if k is an odd positive integer, then every orientation of a regular graph of degree k has a minimum decomposition which contains no vertex which is both the initial vertex of some path in the decomposition and the terminal vertex of some other path in the decomposition. In this paper, the conjecture is established for cubic graphs, and its connection with Kelly's conjecture for tournaments is described.