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

By Juan José Rué Perna, Dimitrios Thilikos Touloupas and Vasiliki Velona

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.Peer Reviewe

Topics: Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta, Computer science--Mathematics, series-parallel graphs, links, knots, generating functions, asymptotic enumeration, map enumeration, Informàtica--Matemàtica
Publisher: 'Elsevier BV'
Year: 2018
DOI identifier: 10.1016/j.endm.2018.06.021
OAI identifier: oai:upcommons.upc.edu:2117/121482
Provided by: UPCommons
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