Tutteʹs 5-flow conjecture for highly cyclically connected cubic graphs

We prove that every bridgeless cubic graph G which has no edge cut with fewer than 5 2 ω − 1 edges that separates two odd cycles of a minimum 2-factor of G has a nowhere-zero 5-flow. This implies that every cubic graph with cyclic connectivity n G ∗ ⩾ 5 2 ω − 1 has a nowhere-zero 5-flow.