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

Juanjo Rué, Dimitrios M. Thilikos, Vasiliki Velona

Research output: Contribution to journalArticlepeer-review


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∈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.

Original languageEnglish (US)
Article number103147
JournalEuropean Journal of Combinatorics
StatePublished - Oct 2020

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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