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Ancestors and descendants in evolving k-tree models


  • Supported by the Austrian Science Foundation (S9608-N23).


We consider several random graph models based on k-trees, which can be generated by applying the probabilistic growth rules “uniform attachment”, “preferential attachment”, or a “saturation”-rule, respectively, but which also can be described in a combinatorial way. For all of these models we study the number of ancestors and the number of descendants of nodes in the graph by carrying out a precise analysis which leads to exact and limiting distributional results. © 2014 Wiley Periodicals, Inc. Random Struct. Alg. 44, 465–489, 2014