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COMBINATORICA
2011
12 years 5 months ago
On the chromatic number of random geometric graphs
Given independent random points X1, . . . , Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n) > 0, we construct a random geometric graph Gn wi...
Colin McDiarmid, Tobias Müller
ADBIS
2003
Springer
95views Database» more  ADBIS 2003»
13 years 10 months ago
Distance Join Queries of Multiple Inputs in Spatial Databases
Let a tuple of n objects obeying a query graph (QG) be called the n-tuple. The “Ddistance-value” of this n-tuple is the value of a linear function of distances of the n objects...
Antonio Corral, Yannis Manolopoulos, Yannis Theodo...
JGT
2008
77views more  JGT 2008»
13 years 5 months ago
List-coloring the square of a subcubic graph
The square G2 of a graph G is the graph with the same vertex set as G and with two vertices adjacent if their distance in G is at most 2. Thomassen showed that for a planar graph ...
Daniel W. Cranston, Seog-Jin Kim
ALGORITHMICA
2008
63views more  ALGORITHMICA 2008»
13 years 5 months ago
The Swap Edges of a Multiple-Sources Routing Tree
Let T be a spanning tree of a graph G and S V (G) be a set of sources. The routing cost of T is the total distance from all sources to all vertices. For an edge e of T, the swap ...
Bang Ye Wu, Chih-Yuan Hsiao, Kun-Mao Chao
APPROX
2011
Springer
242views Algorithms» more  APPROX 2011»
12 years 5 months ago
New Tools for Graph Coloring
How to color 3 colorable graphs with few colors is a problem of longstanding interest. The best polynomial-time algorithm uses n0.2072 colors. There are no indications that colori...
Sanjeev Arora, Rong Ge