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arXiv · 1709.02837

Obstructions to a small hyperbolicity in Helly graphs

Feodor F. Dragan·Heather M. Guarnera
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Abstract

It is known that for every graph $G$ there exists the smallest Helly graph $\cal H(G)$ into which $G$ isometrically embeds ($\cal H(G)$ is called the injective hull of $G$) such that the hyperbolicity of $\cal H(G)$ 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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BibTeXRIS

Feodor F. Dragan, Heather M. Guarnera. 2017-09-08. Obstructions to a small hyperbolicity in Helly graphs. https://doi.org/10.1016/j.disc.2018.10.017

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