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 language | English (US) |
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Pages (from-to) | 283-298 |
Number of pages | 16 |
Journal | Arnold Mathematical Journal |
Volume | 1 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1 2015 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Bollobás-Riordan polynomial
- Duality
- Graphs on surfaces
- Kauffman bracket
- Ribbon graphs
- Tutte polynomial