The graphic additive base conjecture asserts that, for an odd prime 
, the presence of 
edge-disjoint spanning trees
allows every compatible prescription of outdegrees
modulo 
to be realized by a graph orientation.
Jafari (2026) proved the stronger statement for every integer 
. If a connected multigraph 
has 
edge-disjoint spanning trees and 
satisfies
 |
then 
has a graph orientation with 
for every 
. Here 
is the outdegree; loops
are permitted and contribute one to the outdegree.
The revised argument also gives decomposition and flow consequences. Every simple graph with 
edge-disjoint spanning trees
and an edge count divisible by 
decomposes into star graphs 
, for integers 
. In particular, 
-edge connectivity suffices.
For 
, connectedness and an even edge
count suffice. Related sharp bounds concern the circular
flow number.
