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DM
2010
91views more  DM 2010»
15 years 5 months ago
Adjacency posets of planar graphs
In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimensio...
Stefan Felsner, Ching Man Li, William T. Trotter
CORR
2011
Springer
205views Education» more  CORR 2011»
14 years 12 months ago
Random Walk on Directed Dynamic Graphs
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the re...
Oksana Denysyuk, Luis Rodrigues
DM
2010
126views more  DM 2010»
15 years 5 months ago
Asymptotic connectivity of hyperbolic planar graphs
We investigate further the concept of asymptotic connectivity as defined previously by the first author. In particular, we compute an upper bound on the asymptotic connectivity of ...
Patrick Bahls, Michael R. Dipasquale
COMBINATORICS
2006
135views more  COMBINATORICS 2006»
15 years 5 months ago
Drawing a Graph in a Hypercube
A d-dimensional hypercube drawing of a graph represents the vertices by distinct points in {0, 1}d, such that the line-segments representing the edges do not cross. We study lower...
David R. Wood
FOCS
2009
IEEE
15 years 11 months ago
Distance Oracles for Sparse Graphs
Abstract— Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer...
Christian Sommer 0002, Elad Verbin, Wei Yu