Bollobás–Riordan and Relative Tutte Polynomials

Clark Butler, Sergei Chmutov

Research output: Contribution to journalArticle

Abstract

We establish a relation between the Bollobás–Riordan polynomial of a ribbon graph with the relative Tutte polynomial of a plane graph obtained from the ribbon graph using its projection to the plane in a nontrivial way. Also we give a duality formula for the relative Tutte polynomial of dual plane graphs and an expression of the Kauffman bracket of a virtual link as a specialization of the relative Tutte polynomial.

Original languageEnglish (US)
Pages (from-to)283-298
Number of pages16
JournalArnold Mathematical Journal
Volume1
Issue number3
DOIs
StatePublished - Sep 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Bollobás-Riordan polynomial
  • Duality
  • Graphs on surfaces
  • Kauffman bracket
  • Ribbon graphs
  • Tutte polynomial

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