Quasi-tree expansion for the Bollobas-Riordan-Tutte polynomial

Abhijit Champanerkar

Knots in Washington XXVII; 3rd Japan-USA Workshop in Knot Theory
January 9-11, 2009
George Washington University
Washington, DC, USA

Organizers
Yoshiyuki Ohyama (TWCU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Kouki Taniyama (Waseda and GWU), Tatsuya Tsukamoto (Osaka IT), Hao Wu (GWU), Akira Yasuhara (Tokyo GU)

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Quasi-tree expansion for the Bollobas-Riordan-Tutte polynomial
by
Abhijit Champanerkar
College of Staten Island, CUNY
Coauthors: Ilya Kofman and Neal Stoltzfus

Bollobas and Riordan introduced a three-variable polynomial extending the Tutte polynomial to oriented ribbon graphs, which are multi-graphs embedded in oriented surfaces, such that complementary regions (faces) are discs. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. By generalizing Tutte's concept of activity to quasi-trees, we extend the spanning tree expansion of the Tutte polynomial to a quasi-tree expansion of the Bollobas-Riordan-Tutte polynomial.

Paper reference: arXiv:0705.3458

Date received: November 25, 2008