# Extending Tutte and Bollob\'as-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs

@article{Avohou2013ExtendingTA, title={Extending Tutte and Bollob\'as-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs}, author={R. C. Avohou and J. B. Geloun and M. N. Hounkonnou}, journal={arXiv: Geometric Topology}, year={2013} }

The Bollobas-Riordan polynomial [Math. Ann. 323, 81 (2002)] is a universal polynomial invariant for ribbon graphs. We find an extension of this polynomial for a particular family of combinatorial objects called rank 3 weakly-colored stranded graphs. Stranded graphs arise in the study of tensor models for quantum gravity in physics, and generalize graphs and ribbon graphs. We present a seven-variable polynomial invariant of these graphs which obeys a contraction/deletion recursion relationâ€¦Â Expand

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