Knots and Graphs: Two Centuries of Interaction

DOI10.1090/conm/670/13449zbMath1357.57020OpenAlexW2908286568MaRDI QIDQ3178936

Józef H. Przytycki

Publication date: 20 December 2016

Published in: Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/8d219ba45c99962759c6038ed44ad219a4fa0de1

zbMATH Keywords

Hopf algebrasknotsgraphsKauffman polynomialJones polynomialsJones-Conway polynomialalternating link diagramsTait conjecturessetoids\(q\)-polynomial of rooted graphsadequate link diagramsPerko knots

Mathematics Subject Classification ID

Related Items (3)

\(q\)-polynomial invariant of rooted trees ⋮ Strict unimodality of plucking polynomials of rooted trees ⋮ Realization of plucking polynomials

Cites Work

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• \(q\)-polynomial invariant of rooted trees
• Proof of Przytycki's conjecture on matched diagrams
• Closed incompressible surfaces in alternating knot and link complements
• Khovanov homology and the slice genus
• The classification of alternating links
• On the Goertiz matrix of a link
• A Tutte polynomial for signed graphs
• A partial order of links
• Representation of links by braids: A new algorithm
• A polynomial invariant for unoriented knots and links
• A polynomial invariant of oriented links
• A spanning tree expansion of the Jones polynomial
• State models and the Jones polynomial
• Jones polynomials and classical conjectures in knot theory
• Hecke algebra representations of braid groups and link polynomials
• The minimal number of Seifert circles equals the braid index of a link
• Knot polynomials and generalized mutation
• On the Kauffman polynomial of an adequate link
• Non-trivial negative links have positive signature
• Kauffman's polynomial and alternating links
• Applications of Donaldson's theorems to classical knot concordance, homology 3-spheres and property P
• Homology of group systems with applications to knot theory
• Genus of alternating link types
• The Conway polynomial
• Non-trivial positive braids have positive signature
• On a general class of graph polynomials
• An introduction to matching polynomials
• On the signature of a link
• Some links with non-trivial polynomials and their crossing-numbers
• A partial order of knots
• Gauge theory for embedded surfaces. I
• Incidence Hopf algebras
• The coloring of graphs
• On graph invariants given by linear recurrence relations
• Knotted periodic orbits in dynamical systems. I: Lorenz's equations
• Über das Geschlecht von Knoten
• Knots.
• Hopf algebra methods in graph theory
• Catalan states of lattice crossing
• Graph theory and statistical physics
• Quadratische Formen und Verschlingungsinvarianten von Knoten
• Branched covering spaces and the quadratic forms of links
• The Trieste look at Knot Theory
• From Goeritz Matrices to Quasi-alternating Links
• A Dichromatic Polynomial for Weighted Graphs and Link Polynomials
• On Invariants of Graphs with Applications to Knot Theory
• The skein polynomial of a planar star product of two links
• On a Lower Bound for Short Noncontractible Cycles in Embedded Graphs
• ALMOST POSITIVE LINKS HAVE NEGATIVE SIGNATURE
• A polynomial invariant for knots via von Neumann algebras
• A new polynomial invariant of knots and links
• Seifert circles and knot polynomials
• The 2-variable polynomial of cable knots
• On the Degree of the Brandt-Lickorish-Millett-Ho Polynomial of a Link
• Jones polynomials and classical conjectures in knot theory. II
• Braids and the Jones Polynomial
• Invariants of links of Conway type
• Tutte Polynomials and Link Polynomials
• A Family of Links and the Conway Calculus
• The Tait flyping conjecture
• Positive knots have negative signature
• Strong Tutte Functions of Matroids and Graphs
• An index of a graph with applications to knot theory
• Algebraic Graph Theory
• The fourth Skein Module and the Montesinos-Nakanishi Conjecture for 3-algebraic links
• A combinatorial formula for the signature of alternating diagrams
• On the computational complexity of the Jones and Tutte polynomials
• Calculating the 2-variable polynomial for knots presented as closed braids
• Remarks on the history of the classification of knots
• Bipartite knots
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• The t₃, moves conjecture for oriented links with matched diagrams

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