Abstract.
The hyperbolicity \( \delta^* \ge 0 \) of a metric space in Gromov's sense can be viewed as a measure of how "tree-like" the space is, since those spaces for which \( \delta^* = 0 \) holds are precisely the set of (metric) trees. Here, we show that any chordal graph equipped with the usual graph metric is in this sense reasonably tree-like. In particular, we prove that the hyperbolicity of any chordal graph is bounded, and is at most two. Moreover, we characterize those chordal graphs with hyperbolicity one.
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Received February 26, 2000
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Brinkmann, G., Koolen, J. & Moulton, V. On the Hyperbolicity of Chordal Graphs. Annals of Combinatorics 5, 61–69 (2001). https://doi.org/10.1007/s00026-001-8007-7
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DOI: https://doi.org/10.1007/s00026-001-8007-7