Tree Diagrams for String Links

TL;DR

This paper classifies the tree structures that can be realized as intersection graphs of string link diagrams, advancing the understanding of their combinatorial properties in the context of finite type invariants.

Contribution

It provides a complete classification of trees that serve as intersection graphs for string link diagrams, a novel result in the study of finite type invariants.

Findings

Identifies all possible trees that can be intersection graphs of string links.

Establishes criteria for when a tree can be realized as an intersection graph.

Contributes to the combinatorial understanding of string link invariants.

Abstract

In previous work, the author defined the intersection graph of a chord diagram associated with string links (as in the theory of finite type invariants). In this paper, we classify the trees which can be obtained as intersection graphs of string link diagrams.