Arrow ribbon graphs

Robert Bradford, Clark Butler, Sergei Chmutov

Research output: Contribution to journalReview article

2 Scopus citations

Abstract

We introduce an additional arrow structure on ribbon graphs. We extend the dichromatic polynomial to ribbon graphs with this structure. This extended polynomial satisfies the contractiondeletion relations and behaves naturally with respect to the partial duality of ribbon graphs. From a virtual link, we construct an arrow ribbon graph whose extended dichromatic polynomial specializes to the arrow polynomial of the virtual link recently introduced by H. Dye and L. Kauffman. This result generalizes the classical Thistlethwaite theorem to the arrow polynomial of virtual links.

Original languageEnglish (US)
Article number1240002
JournalJournal of Knot Theory and its Ramifications
Volume21
Issue number13
DOIs
StatePublished - Nov 1 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • BollobásRiordan polynomial
  • Graphs on surfaces
  • Tutte polynomial
  • arrow polynomial
  • dichromatic polynomial
  • duality
  • ribbon graphs
  • virtual links

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