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arXiv · 0705.3458

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

Abhijit Champanerkar·Ilya Kofman·Neal Stoltzfus
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Abstract

Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. The Bollobás-Riordan-Tutte polynomial is a three-variable polynomial that extends the Tutte polynomial to oriented ribbon graphs. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We generalize the spanning tree expansion of the Tutte polynomial to a quasi-tree expansion of the Bollobás-Riordan-Tutte polynomial.

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Abhijit Champanerkar, Ilya Kofman, Neal Stoltzfus. 2011-06-29. Quasi-tree expansion for the Bollobás-Riordan-Tutte polynomial. https://doi.org/10.1112/blms%2Fbdr034

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