Geodesic
Graphs with small additive stretch number
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 291-301

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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.
Keywords: stretch number, distance hereditary graph, forbidden induced subgraph 
Rautenbach, Dieter. Graphs with small additive stretch number. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 291-301. http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a10/
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