87 research outputs found
Pseudo-random graphs
Random graphs have proven to be one of the most important and fruitful
concepts in modern Combinatorics and Theoretical Computer Science. Besides
being a fascinating study subject for their own sake, they serve as essential
instruments in proving an enormous number of combinatorial statements, making
their role quite hard to overestimate. Their tremendous success serves as a
natural motivation for the following very general and deep informal questions:
what are the essential properties of random graphs? How can one tell when a
given graph behaves like a random graph? How to create deterministically graphs
that look random-like? This leads us to a concept of pseudo-random graphs and
the aim of this survey is to provide a systematic treatment of this concept.Comment: 50 page
Cannon-Thurston Maps for Pared Manifolds of Bounded Geometry
Let N^h be a hyperbolic 3-manifold of bounded geometry corresponding to a
hyperbolic structure on a pared manifold (M,P). Further, suppose that
(\partial{M} - P) is incompressible, i.e. the boundary of M is incompressible
away from cusps. Further, suppose that M_{gf} is a geometrically finite
hyperbolic structure on (M,P). Then there is a Cannon- Thurston map from the
limit set of M_{gf} to that of N^h. Further, the limit set of N^h is locally
connected. This answers in part a question attributed to Thurston.Comment: 57 pages, 4 figures, Final version incorporating referee's comments.
To appear in Geometry and Topolog
Cannon-Thurston maps for pared manifolds of bounded geometry
Let Nh ∈, H(M, P) be a hyperbolic structure of bounded geometry on a pared manifold such that each component of ∂0M = ∂M - P is incompressible. We show that the limit set of Nh is locally connected by constructing a natural Cannon-Thurston map. This provides a unified treatment, an alternate proof and a generalization of results due to Cannon and Thurston, Minsky, Bowditch, Klarreich and the author
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
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