  We introduce a new type of preferential attachment tree that includes choices
in its evolution, like with Achlioptas processes. At each step in the growth of
the graph, a new vertex is introduced. Two possible neighbor vertices are
selected independently and with probability proportional to degree. Between the
two, the vertex with smaller degree is chosen, and a new edge is created. We
determine with high probability the largest degree of this graph up to some
additive error term.
