There exist graphs with super-exponential Ramsey multiplicity constant

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Suicide Ideation Detection via Social and Temporal User Representations using Hyperbolic Learning (2021, methodology): “In Table 1, we outline quantitative analyses of the social network G and report Gromov’s δhyperbolicity of the graph (Jonckheere et al., 2008).”
Gromov hyperbolicity in Cartesian product graphs (2010, background): “The study of mathematical properties of Gromov hyperbolic spaces and its applications is a topic of recent and increasing interest in graph theory; see, for instance [2, 3, 4, 7, 8, 9, 11, 12, 18, 19, 20, 21, 22, 24, 26, 27, 29, 30].”
Chordality and hyperbolicity of a graph (2009, background): “This concept not only turns out to be strikingly useful in coarse geometry but also becomes more and more important in many applied fields like networking and phylogenetics [24, 25, 26, 27, 39, 41, 42, 43, 45, 53, 69, 70, 73, 88].”
Machine Learning on Graphs: A Model and Comprehensive Taxonomy (2020, background): “Gromov’s four-point condition [59]), an interesting open research direction is how to pick or learn the right geometry for a given discrete graph.”
Gromov hyperbolic cubic graphs (2012, background): “The study of mathematical properties of Gromov hyperbolic spaces and its applications is a topic of recent and increasing interest in graph theory; see, for instance [4, 5, 6, 7, 10, 11, 14, 24, 25, 26, 28, 30, 31, 34, 35, 37, 38, 39, 40, 42].”