S.V.Chmutov, S.V.Duzhin, S.K.Lando,
Vassiliev knot invariants} II. Intersection graph conjecture for trees,
The principal tool in this sequence of papers is the intersection graph of a
chord diagram: this is obtained by taking a vertex for each chord in the
diagram and an edge between two vertices if the corresponding chords
intersect. The intersection graph conjecture is that weight systems
(functionals on chord diagrams satisfying the 4T and 1T relations) depend
only on the intersection graphs of diagrams. This has been verified for
weight systems up to degree eight and for weight systems coming from the
defining representations of $so(n)$ and $gl(n)$. This paper (second in the
series) consists of proving the conjecture for the case that the
intersection graph is a tree.