Proximity to ℓpℓp and c0c0 in Banach spaces

We construct a class of minimal trees and use these trees to establish a number of coloring theorems on general trees. Among the applications of these trees and coloring theorems are quantification of the Bourgain ℓpℓp and c0c0 indices, dualization of the Bourgain c0c0 index, establishing sharp positive and negative results for constant reduction, and estimating the Bourgain ℓpℓp index of an arbitrary Banach space X in terms of a subspace Y   and the quotient X/YX/Y.