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Fields 110(3), 277–285 (1998). pdf 13. J. Pitman, Coalescent random forests. J. Combin. Theory Ser. A 85, 165–193 (1999). pdf 14. A. Rényi, Some remarks on the theory of trees. Magyar Tud. Akad. Mat. Kutató Int. Közl. 4, 73–85 (1959) 15. A. Rényi, G. Szekeres, On the height of trees. J. Austral. Math. Soc. 7, 497–507 (1967). N;k be the distance-k graph of the N-fold star power of G. N;k converges to a centered Bernoulli distribution, 1=2ı 1 C 1=2ı1. The proof is based in a fourth moment lemma for convergence to a centered Bernoulli distribution.

STEP i: ? If Di ¤ ; then choose v 2 Di with highest priority (if there is a tie, pick the vertex with smallest label among highest-priority vertices). v/ \ Ui /. Ui ; p/, independently of all previous steps. Let EiC1 D Ei and let UiC1 D Ui n DiC1 . Ui ; i 0/. The order of exploration yields the following property of the search process. Suppose Di D ; for a given i. i C 1/. i C 1/, the search process will fully explore the component containing the smallest labelled vertex of DiC1 before exploring any vertex in any other component.

Pdf 6. E. Baur, On a ternary coalescent process. ALEA Lat. Am. J. Probab. Math. Stat. 10(2), 561–589 (2013). pdf 7. M. Biskup, L. A. Smith, Large-deviations/thermodynamic approach to percolation on the complete graph. Random Struct. Algorithms 31(3), 354–370 (2007). org/ abs/math/0506255 Discrete Coalescents 45 8. L. Devroye, A note on the height of binary search trees. J. Assoc. Comput. Mach. 33(3), 489–498 (1986). pdf 9. M. Frieze, On the value of a random minimum spanning tree problem. Discret.

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