On the Expected Maximum Degree of Gabriel and Yao Graphs

Details On the Expected Maximum Degree of Gabriel and Yao Graphs On the Expected Maximum Degree of Gabriel and Yao Graphs

2009-05-21

arxiv.org/abs/0905.3584v1

Computer Science

Computational Geometry

20 pages, 10 figures

Scientific paper

Motivated by applications of Gabriel graphs and Yao graphs in wireless ad-hoc
networks, we show that the maximal degree of a random Gabriel graph or Yao
graph defined on $n$ points drawn uniformly at random from a unit square grows
as $\Theta (\log n / \log \log n)$ in probability.

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