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

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Title:	Structure and enumeration of K4-minor-free links and link diagrams
Author:	Rué Perna, Juan José; Thilikos Touloupas, Dimitrios; Velona, Vasiliki
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
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.
Abstract:	Peer Reviewed
Subject(s):	-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
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Document type:	Article - Submitted version Article
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