Ancestors and descendants in evolving k‐tree models

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