In view of Lemma C.9, there are four possible cases in total aboutα∩β̸=∅, α̸=βand α′ ∩β ′ ̸=∅, α ′ ̸=β ′

andβ ′ = (t′ 1t′ 2)∪(t ′ 3t′ 4), where s2 ands 3 are incident toα’s degree 2 vertex,t 2 andt 3 are incident toβ’s degree 2 vertex,s ′ 2 ands ′ 3 are incident toα ′’s degree 2 verte