On the expected maximum degree of Gabriel and Yao graphs
Luc Devroye, Joachim Gudmundsson, Pat Morin · Advances in Applied Probability · 2009
Motivated by applications of Gabriel graphs and Yao graphs in wireless ad-hoc networks, we show that the maximum 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.