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Article Dans Une Revue European Journal of Combinatorics Année : 2020

Structure and enumeration of $K_4$- minor-free links and link-diagrams

Résumé

We study the class $\mathcal{L}$ of link-types that admit a $K_4$-minor-free diagram, i.e., they can be projected on the plane so that the resulting graph does not contain any subdivision of $K_{4}$. We prove that $\mathcal{L}$ is the closure of a subclass of torus links under the operation of connected sum. Using this structural result, we enumerate $\mathcal{L}$ (and subclasses of it), with respect to the minimum number of crossings or edges in a projection of $L\in \mathcal{L}$. Further, we obtain counting formulas and asymptotic estimates for the connected $K_4$-minor-free link-diagrams, minimal $K_4$-minor-free link-diagrams, and $K_4$-minor-free diagrams of the unknot.
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Dates et versions

hal-03002619 , version 1 (20-11-2020)

Identifiants

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Juanjo Rué, Dimitrios M. Thilikos, Vasiliki Velona. Structure and enumeration of $K_4$- minor-free links and link-diagrams. European Journal of Combinatorics, 2020, 89, pp.103147. ⟨10.1016/j.ejc.2020.103147⟩. ⟨hal-03002619⟩
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