  In 1972 Tutte famously conjectured that every 4-edge-connected graph has a
nowhere zero 3-flow; this is known to be equivalent to every 5-regular,
4-edge-connected graph having an edge orientation in which every in-degree is
either 1 or 4. Jaeger conjectured a generalization of Tutte's conjecture,
namely, that every $4p+1$-regular, $4p$-edge-connected graph has an edge
orientation in which every in-degree is either $p$ or $3p+1$. Inspired by the
work of Pralat and Wormald investigating $p=1$, for $p=2$ we show this holds
asymptotically almost surely for random 9-regular graphs. It follows that the
conjecture holds for almost all 9-regular, 8-edge-connected graphs. These
results make use of the technical small subgraph conditioning method.
