Pósa-condition and nowhere-zero 3-flows

Let GG be a simple graph on nn vertices and π(G)=(d1,d2,…,dn)π(G)=(d1,d2,…,dn) be the degree sequence of GG, where n≥3n≥3 and d1≤d2≤⋯≤dnd1≤d2≤⋯≤dn. The classical Pósa’s theorem states that if dm≥m+1dm≥m+1 for 1≤m