Structure and Enumeration of $K4$-minor-free links and link diagrams - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Electronic Notes in Discrete Mathematics Year : 2018

Structure and Enumeration of $K4$-minor-free links and link diagrams

Abstract

We study the class 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 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 minimal number of crossings or edges in a projection of L ∈ L. Further, we enumerate (both exactly and asymptotically) all connected K 4-minor-free link diagrams, all minimal connected K 4-minor-free link diagrams, and all K 4-minor-free diagrams of the unknot.
Fichier principal
Vignette du fichier
spknots_DMC.pdf (244.51 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

lirmm-01890505 , version 1 (08-10-2018)

Identifiers

Cite

Juanjo Rué, Dimitrios M. Thilikos, Vasiliki Velona. Structure and Enumeration of $K4$-minor-free links and link diagrams. Electronic Notes in Discrete Mathematics, 2018, 68, pp.119-124. ⟨10.1016/j.endm.2018.06.021⟩. ⟨lirmm-01890505⟩
137 View
90 Download

Altmetric

Share

Gmail Facebook X LinkedIn More