THISTLETHWAITE'S THEOREM FOR VIRTUAL LINKS

DOI10.1142/S0218216508006609zbMath1163.57001arXiv0704.1310MaRDI QIDQ3602959

Jeremy Voltz, Sergei Chmutov

Publication date: 12 February 2009

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.1310

zbMATH Keywords

ribbon graphsKauffman bracketvirtual knots and linksBollobas-Riordan polynomial

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Relations of low-dimensional topology with graph theory (57M15)

Related Items (22)

On the Seifert graphs of a link diagram and its parallels ⋮ The Jones-Krushkal polynomial and minimal diagrams of surface links ⋮ From matrix pivots to graphs in surfaces: exploring combinatorics through partial duals ⋮ Non-orientable quasi-trees for the Bollobás-Riordan polynomial ⋮ Partial duals of plane graphs, separability and the graphs of knots ⋮ Unsigned state models for the Jones polynomial ⋮ Expansions for the Bollobás-Riordan polynomial of separable ribbon graphs ⋮ Counterexamples to a conjecture by Gross, Mansour and Tucker on partial-dual genus polynomials of ribbon graphs ⋮ Characterization of regular checkerboard colourable twisted duals of ribbon graphs ⋮ A BRACKET POLYNOMIAL FOR GRAPHS, III: VERTEX WEIGHTS ⋮ Relative Tutte Polynomials of Tensor Products of Coloured Graphs ⋮ Bollobás-Riordan and relative Tutte polynomials ⋮ A BRACKET POLYNOMIAL FOR GRAPHS, II: LINKS, EULER CIRCUITS AND MARKED GRAPHS ⋮ The chromatic polynomial of fatgraphs and its categorification ⋮ ARROW RIBBON GRAPHS ⋮ A characterization of partially dual graphs ⋮ Relative Tutte Polynomials for Coloured Graphs and Virtual Knot Theory ⋮ Characterizations of bipartite and Eulerian partial duals of ribbon graphs ⋮ Excluded Minors and the Ribbon Graphs of Knots ⋮ Generalized duality for graphs on surfaces and the signed Bollobás-Riordan polynomial ⋮ Matroids, delta-matroids and embedded graphs ⋮ Partial duality and Bollobás and Riordan's ribbon graph polynomial

Cites Work

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• A polynomial of graphs on surfaces
• A Tutte polynomial for signed graphs
• A spanning tree expansion of the Jones polynomial
• Finite-type invariants of classical and virtual knots
• Virtual knot theory
• A Polynomial Invariant of Graphs On Orientable Surfaces
• New Invariants in the Theory of Knots

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