| Random Triangulations and Trees (1999) | |||||||||||||||
Abstract | |||||||||||||||
| gulation ø of K, let d i denote the degree of vertex v i , the number of (the n \Gamma 3 internal) diagonals of ø that are incident with v i . We study \Delta n (ø) = max(d i ; i = 0; : : : ; n \Gamma 1) ; (1) the maximal degree of the vertices. It is clear that 2 \Delta n n \Gamma 3. To see how \Delta n behaves across the family of triangulations, we treat it as a random variable under the uniform probability on T n . By symmetry, each d i has the same distribution, but they are not independent because, e.g., d 0 + \Delta \Delta \Delta + d<F | |||||||||||||||
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