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arXiv · 1806.07855

Structure and enumeration of K4-minor-free links and link-diagrams

Juanjo Rué·Dimitrios M. Thilikos·Vasiliki Velona
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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.

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Juanjo Rué, Dimitrios M. Thilikos, Vasiliki Velona. 2018-06-20. Structure and enumeration of K4-minor-free links and link-diagrams. https://arxiv.org/abs/1806.07855

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