Article - post-print
In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term relations).
Mellor, B., 2008: Tree Diagrams for String Links II: Determining Chord Diagrams. J. Knot Theory Ramif., 17.6, 649-664, arXiv:math/0408286.