The additive stretch number $s_{add}(G)$ of a graph G is the maximum difference of the lengths of a longest induced path and a shortest induced path between two vertices of G that lie in the same component of G.We prove some properties of minimal forbidden configurations for the induced-hereditary classes of graphs G with $s_{add}(G) ≤ k$ for some k ∈ N₀ = {0,1,2,...}. Furthermore, we derive characterizations of these classes for k = 1 and k = 2.
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