Speaker:  Gábor Hetyei, UNC Charlotte

Title:  Brylawski's tensor product formula for Tutte polynomials of colored graphs

Abstract: 

The tensor product of a graph and of a pointed graph is obtained by replacing each edge of the first graph with a copy of the second. In his expository talk we will explore a colored generalization of Brylawski's formula  for the Tutte polynomial of the tensor product of a graph with a pointed graph and its applications.  Using Tutte's original (activity-based) definition of the Tutte polynomial we will provide a simple proof of Brylawski's formula. This can be easily generalized to the colored Tutte polynomials introduced by Bollobás and Riordan. Consequences include formulas for Jones polynomials of (virtual) knots and for invariants of composite networks in which some major links are identical subnetworks in themselves.



All results presented are joint work with Yuanan Diao, some of them are also joint work with Kenneth Hinson. The relevant definitions and the fundamental results used will be carefully explained.  

G. Hetyei will be a visitor of R. Ehrenborg and M. Readdy the first week of March.