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The Cartographer
Obstructions to a small hyperbolicity in Helly graphs
September 08, 2017 Β· Declared Dead Β· π Discrete Mathematics
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Authors
Feodor F. Dragan, Heather M. Guarnera
arXiv ID
1709.02837
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.DM,
math.CO
Citations
11
Venue
Discrete Mathematics
Last Checked
4 months ago
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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