# Obstructions to a small hyperbolicity in Helly graphs

It is known that for every graph G there exists the smallest Helly graph H(G) into which G isometrically embeds ( H(G) is called the injective hull of G) such that the hyperbolicity of H(G) is equal to the hyperbolicity of G. Motivated by this, we investigate structural properties of Helly graphs that govern their hyperbolicity and identify three isometric subgraphs of the King-grid as structural obstructions to a small hyperbolicity in Helly graphs.

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