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 minimal number of crossings or edges in a projection of L∈L. Further, we enumerate (both exactly and asymptotically) all connected K4-minor-free link diagrams, all minimal connected K4-minor-free link diagrams, and all K4-minor-free diagrams of the unknot.

Original languageEnglish (US)
Pages (from-to)119-124
Number of pages6
JournalElectronic Notes in Discrete Mathematics
StatePublished - Jul 2018


  • asymptotic enumeration
  • generating functions
  • knots
  • links
  • map enumeration
  • series-parallel graphs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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