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COMBINATORICS
2006
124views more  COMBINATORICS 2006»
13 years 7 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 7 months ago
Bounded-Degree Graphs can have Arbitrarily Large Slope Numbers
János Pach, Dömötör Pá...
GD
1998
Springer
13 years 11 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 7 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»
13 years 2 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