Generalized duality for graphs on surfaces and the signed Bollobás-Riordan polynomial

DOI10.1016/j.jctb.2008.09.007zbMath1172.05015arXiv0711.3490OpenAlexW2006818453MaRDI QIDQ1026002

Sergei Chmutov

Publication date: 23 June 2009

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.3490

zbMATH Keywords

dualityJones polynomialribbon graphsgraphs on surfacesBollobás-Riordan polynomialembedded graphpartial dualityvirtual linksribbon graph polynomial

Mathematics Subject Classification ID

Related Items (66)

Checkerboard colourable twuals ⋮ Twisted duality for embedded graphs ⋮ Parallel edges in ribbon graphs and interpolating behavior of partial-duality polynomials ⋮ Counterexamples to the interpolating conjecture on partial-dual genus polynomials of ribbon graphs ⋮ Partial duality for ribbon graphs. III: A gray code algorithm for enumeration ⋮ Extending the Tutte and Bollobás–Riordan polynomials to rank 3 weakly coloured stranded graphs ⋮ New dualities from old: generating geometric, Petrie, and Wilson dualities and trialities of ribbon graphs ⋮ Ribbon graph minors and low-genus partial duals ⋮ On the Seifert graphs of a link diagram and its parallels ⋮ Excluded checkerboard colourable ribbon graph minors ⋮ Handle slides for delta-matroids ⋮ Parametric representation of rank d tensorial group field theory: Abelian models with kinetic term ∑sps+μ ⋮ Partial-dual Euler-genus distributions for bouquets with small Euler genus ⋮ A-trails of embedded graphs and twisted duals ⋮ Enumerating graph embeddings and partial-duals by genus and Euler genus ⋮ Twist polynomials of delta-matroids ⋮ Genus ranges of 4-regular rigid vertex graphs ⋮ Partial-dual polynomials and signed intersection graphs ⋮ From matrix pivots to graphs in surfaces: exploring combinatorics through partial duals ⋮ The structure of delta-matroids with width one twists ⋮ Partial-twuality polynomials of delta-matroids ⋮ Delta-matroids whose twist polynomials are monomials ⋮ Non-orientable quasi-trees for the Bollobás-Riordan polynomial ⋮ Signed permutohedra, delta‐matroids, and beyond ⋮ Evaluations of Topological Tutte Polynomials ⋮ The number of quasi-trees in fans and wheels ⋮ Partial duals of plane graphs, separability and the graphs of knots ⋮ A Topologically Complete Theory of Weaving ⋮ Counterexamples to a conjecture by Gross, Mansour and Tucker on partial-dual genus polynomials of ribbon graphs ⋮ Constructive tensor field theory: the \(T_{4}^{4}\) model ⋮ Characterization of regular checkerboard colourable twisted duals of ribbon graphs ⋮ Bipartite partial duals and circuits in medial graphs ⋮ A survey on the Turaev genus of knots ⋮ The transition matroid of a 4-regular graph: an introduction ⋮ Relative Tutte Polynomials of Tensor Products of Coloured Graphs ⋮ Bollobás-Riordan and relative Tutte polynomials ⋮ Partial duality for ribbon graphs. I: distributions ⋮ A quasi-tree expansion of the Krushkal polynomial ⋮ ARROW RIBBON GRAPHS ⋮ A characterization of partially dual graphs ⋮ Transition polynomial as a weight system for binary delta-matroids ⋮ Topological graph polynomial and quantum field theory. II: Mehler kernel theories ⋮ REDUCED RELATIVE TUTTE, KAUFFMAN BRACKET AND JONES POLYNOMIALS OF VIRTUAL LINK FAMILIES ⋮ Topological graph polynomials and quantum field theory. I: Theory kernel theories ⋮ A Turaev surface approach to Khovanov homology ⋮ A 2-isomorphism theorem for delta-matroids ⋮ A recipe theorem for the topological Tutte polynomial of Bollobás and Riordan ⋮ Graphical virtual links and a polynomial for signed cyclic graphs ⋮ Relative Tutte Polynomials for Coloured Graphs and Virtual Knot Theory ⋮ Characterizations of bipartite and Eulerian partial duals of ribbon graphs ⋮ Partial duality for ribbon graphs. II: Partial-twuality polynomials and monodromy computations ⋮ Lagrangian subspaces, delta-matroids, and four-term relations ⋮ Excluded Minors and the Ribbon Graphs of Knots ⋮ Types of embedded graphs and their Tutte polynomials ⋮ On a conjecture of Gross, Mansour and Tucker ⋮ Graphs, Links, and Duality on Surfaces ⋮ Extremal embedded graphs ⋮ Planar diagrams for local invariants of graphs in surfaces ⋮ Matroids, delta-matroids and embedded graphs ⋮ Eulerian and even-face ribbon graph minors ⋮ The multivariate signed Bollobás-Riordan polynomial ⋮ Partial duality and Bollobás and Riordan's ribbon graph polynomial ⋮ Eulerian and bipartite binary delta-matroids ⋮ Partial duality of hypermaps ⋮ Generalization of the Bollobás-Riordan polynomial for tensor graphs ⋮ Inductive tools for connected delta-matroids and multimatroids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Expansions for the Bollobás-Riordan polynomial of separable ribbon graphs
• Plane and projective meanders
• On the Jones polynomials of checkerboard colorable virtual links
• A polynomial of graphs on surfaces
• Densely embedded graphs
• The construction and classification of self-dual spherical polyhedra
• A Tutte polynomial for signed graphs
• Embeddings of graphs with no short noncontractible cycles
• The multivariate signed Bollobás-Riordan polynomial
• Partial duality and Bollobás and Riordan's ribbon graph polynomial
• The virtual cohomological dimension of the mapping class group of an orientable surface
• A spanning tree expansion of the Jones polynomial
• The decorated Teichmüller space of punctured surfaces
• A simple proof of the Murasugi and Kauffman theorems on alternating links
• A Hamilton cycle in the Cayley graph of the \(\langle 2,p,3 \rangle\) presentation of PSL\(_ 2(p)\)
• Span of the Jones polynomial of an alternating virtual link
• Ribbon graphs and their invariants derived from quantum groups
• Virtual knot theory
• Knot invariants and the Bollobás-Riordan polynomial of embedded graphs
• The chromatic polynomial of fatgraphs and its categorification
• The Jones polynomial and graphs on surfaces
• Hamiltonicity of cubic Cayley graphs
• Introduction to Vassiliev Knot Invariants
• THISTLETHWAITE'S THEOREM FOR VIRTUAL LINKS
• New Invariants in the Theory of Knots
• Is Selfduality Involutory?
• Parity in knot theory
• On the surface duality of linear graphs

This page was built for publication: Generalized duality for graphs on surfaces and the signed Bollobás-Riordan polynomial