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arXiv · 0905.3584

On the Expected Maximum Degree of Gabriel and Yao Graphs

Luc Devroye·Joachim Gudmundsson·Pat Morin
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Abstract

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 $Θ(\log n / \log \log n)$ in probability.

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Luc Devroye, Joachim Gudmundsson, Pat Morin. 2009-05-21. On the Expected Maximum Degree of Gabriel and Yao Graphs. https://arxiv.org/abs/0905.3584

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