Random Regular Graphs are not Asymptotically Gromov Hyperbolic
نویسنده
چکیده
In this paper we prove that random d–regular graphs with d ≥ 3 have traffic congestion of the order O(n log3d−1(n)) where n is the number of nodes and geodesic routing is used. We also show that these graphs are not asymptotically δ–hyperbolic for any non–negative δ almost surely as n→∞.
منابع مشابه
Traffic Congestion in Expanders and (p, δ)-Hyperbolic Spaces
In this paper we define the notion of (p, δ)–Gromov hyperbolic space where we relax Gromov slimness condition to allow that not all but a positive fraction of all the triangles are δ–slim. Furthermore, we study their traffic congestion under geodesic routing. We also construct a constant degree family of expanders with congestion Θ(n) in contrast to random regular graphs that have congestion O(...
متن کاملNon Hyperbolicity in Random Regular Graphs and their Traffic Characteristics
In this paper we prove that random d–regular graphs with d ≥ 3 have traffic congestion of the order O(n logd−1(n)) where n is the number of nodes and geodesic routing is used. We also show that these graphs are not asymptotically δ–hyperbolic for any non–negative δ almost surely as n→∞.
متن کاملTraffic Congestion in Expanders, $(p,\delta)$--Hyperbolic Spaces and Product of Trees
In this paper we define the notion of (p, δ)–Gromov hyperbolic space where we relax Gromov’s slimness condition to allow that not all but a positive fraction of all triangles are δ–slim. Furthermore, we study maximum vertex congestion under geodesic routing and show that it scales as Ω(pn/D n) where Dn is the diameter of the graph. We also construct a constant degree family of expanders with co...
متن کاملLack of Hyperbolicity in Asymptotic Erdös-Renyi Sparse Random Graphs
In this work, we prove that the giant component of the Erdös–Renyi random graph G(n, c/n) for c a constant greater than 1 (sparse regime), is not Gromov δ–hyperbolic for any δ with probability tending to one as n → ∞. We present numerical evidence to show that the “fat” triangles that rule out δ–hyperbolicity are in fact abundant in these graphs. We also present numerical evidence showing that,...
متن کاملOptimal Cycle Codes Constructed From Ramanujan Graphs
We aim here at showing how some known Ramanujan Cayley graphs yield error-correcting codes that are asymptotically optimal in the class of cycle codes of graphs. The main reason why known constructions of Ramanujan graphs yield good cycle codes is that the number of their cycles of a given length behaves essentially like that of random regular graphs. More precisely we show that for actual cons...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1203.5069 شماره
صفحات -
تاریخ انتشار 2012