  A directed cycle double cover of a graph G is a family of cycles of G, each
provided with an orientation, such that every edge of G is covered by exactly
two oppositely directed cycles. Explicit obstacles to the existence of a
directed cycle double cover in a graph are bridges. Jaeger conjectured that
bridges are actually the only obstacles. One of the difficulties in proving the
Jaeger's conjecture lies in discovering and avoiding obstructions to partial
strategies that, if successful, create directed cycle double covers. In this
work, we suggest a way to circumvent this difficulty. We formulate a conjecture
on graph connections, whose validity follows by the successful avoidance of one
cut-type obstruction that we call cut-obstacles. The main result of this work
claims that our 'cut-obstacles avoidance conjecture' already implies Jaeger's
directed cycle double cover conjecture.
