The purpose of this discussion is to give a proof of Theorem 6 in “Nearly–light cycles in embedded graphs and crossing–critical graphs” [1]. Since this is clearly not intended as a stand–alone manuscript, but as an addendum to [1], we proceed right away to state and prove Theorem 6 in that paper. Theorem 1 (Theorem 6 in [1]). For each ε > 0 and integer χ ≤ 2 there exist `0 := `0(ε, χ), ∆0 := ∆0(ε, χ), c := c(ε, χ) with the following property. Let G = (V, E) be a simple connected graph with… CONTINUE READING