English

Quasi-tree expansion for the Bollob\'as-Riordan-Tutte polynomial

Combinatorics 2016-08-02 v2 Geometric Topology

Abstract

Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. The Bollob\'as-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 Bollob\'as-Riordan-Tutte polynomial.

Keywords

Cite

@article{arxiv.0705.3458,
  title  = {Quasi-tree expansion for the Bollob\'as-Riordan-Tutte polynomial},
  author = {Abhijit Champanerkar and Ilya Kofman and Neal Stoltzfus},
  journal= {arXiv preprint arXiv:0705.3458},
  year   = {2016}
}

Comments

This version to be published in the Bulletin of the London Mathematical Society. 17 pages, 4 figures