Structure and enumeration of K4-minor-free links and link-diagrams
Combinatorics
2020-04-28 v3
Abstract
We study the class L of link-types that admit a K4-minor-free diagram, i.e., they can be projected on the plane so that the resulting graph does not contain any subdivision of K4. We prove that L is the closure of a subclass of torus links under the operation of connected sum. Using this structural result, we enumerate L and subclasses of it, with respect to the minimum number of crossings or edges in a projection of L' in L. Further, we obtain counting formulas and asymptotic estimates for the connected K4-minor-free link-diagrams, minimal K4-minor-free link-diagrams, and K4-minor-free diagrams of the unknot.
Cite
@article{arxiv.1806.07855,
title = {Structure and enumeration of K4-minor-free links and link-diagrams},
author = {Juanjo Rué and Dimitrios M. Thilikos and Vasiliki Velona},
journal= {arXiv preprint arXiv:1806.07855},
year = {2020}
}
Comments
Final version. To appear in European Journal of Combinatorics