I'm sorry to disturb you but I really got stuck! I can't find any clear and, somewhat, complete reference for this topic.

I'm looking for a book, or review, or survey or course notes regarding "Hyperbolic Graph Theory": in this way I hope to find some description of general properties or solving techniques for hyperbolic graphs. If search on google, usually I find stuff related to groups or metric spaces or Cayley graphs but this is not what I'm looking for.

I could find only this talk "http://homepages.warwick.ac.uk/~maslar/talkOW10.pdf" and just this short paper "http://homepages.warwick.ac.uk/~maslar/OWreport10.pdf"

Thanks in advance!!

  • $\begingroup$ Could you clarify what kind of general properties or solving technique are you looking for. Most of the results about hyperbolic Cayley graphs will apply to all graphs. I am not sure you realized this, but all finite graphs are hyperbolic, which means that most combinatorial questions in graph theory are useless in the context of hyperbolic graphs. $\endgroup$ – Moishe Kohan Feb 10 '14 at 20:01
  • $\begingroup$ Hi! I know that every finite graph is hyperbolic: indeed, I'm studying infinite hyperbolic graphs. This means that I'm interested more in the geometrical point of view than in the combinatorical one, e.g. concerning questions such as the non-amenability or the behaviour at the (Poisson) boundary of the graph. So far I have dealt mainly with plane hyperbolic graphs, looking for conditions that would force the graph to have bounded face lengths. Since I've just started facing this topic, I would like to get an overall view about hyperbolic graphs, learning main theorems and definitions. $\endgroup$ – edwineveningfall Feb 11 '14 at 14:14
  • $\begingroup$ Take a look at this paper: wisdom.weizmann.ac.il/~itai/stflouraug24.pdf, maybe you can find something useful there. $\endgroup$ – Moishe Kohan Feb 11 '14 at 15:13
  • $\begingroup$ Thanks a lot for the link!!! Do you also know some reference not focusing on probability? For instance, what about hyperbolic Cayley graphs? (also if I have not considered them in the beginning but I'm desperate) I know it's a much wider subject, but so far I've only found group-theoretic oriented sources and not graph-theoretic ones. $\endgroup$ – edwineveningfall Feb 11 '14 at 16:06
  • $\begingroup$ Paper by Kaimanovich on Poisson boundary of hyperbolic groups (arxiv.org/pdf/math/9802132.pdf) is mostly non-group theoretic (but heavy on probability!). $\endgroup$ – Moishe Kohan Feb 11 '14 at 16:09

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