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COMBINATORICS
2006
124views more  COMBINATORICS 2006»
13 years 3 months ago
Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness
Abstract. The geometric thickness of a graph G is the minimum integer k such that there is a straight line drawing of G with its edge set partitioned into k plane subgraphs. Eppste...
János Barát, Jirí Matousek, D...
COMBINATORICS
2006
134views more  COMBINATORICS 2006»
13 years 3 months ago
Bounded-Degree Graphs can have Arbitrarily Large Slope Numbers
János Pach, Dömötör Pá...
GD
1998
Springer
13 years 7 months ago
Geometric Thickness of Complete Graphs
We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straightline edges and assign each edge to a lay...
Michael B. Dillencourt, David Eppstein, Daniel S. ...
CORR
2010
Springer
190views Education» more  CORR 2010»
13 years 3 months ago
Overlap properties of geometric expanders
The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) (0, 1] such that no matter how we map the vertices of H into Rd , there is a point covered...
Jacob Fox, Mikhail Gromov, Vincent Lafforgue, Assa...
TMC
2011
131views more  TMC 2011»
12 years 10 months ago
In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs
—We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Âð1Þ time units per histogram sample on a ra...
Srikanth K. Iyer, D. Manjunath, R. Sundaresan