## Abstract

We introduce a generalization of the Krushkal polynomial to nonorientable surfaces, and prove that this polynomial has a natural quasi-tree expansion. This generalized Krushkal polynomial contains the Bollobás–Riordan polynomial of a (possibly nonorientable) ribbon graph as a specialization. The quasi-tree expansion proven here then extends the recent quasi-tree expansions of the Bollobás–Riordan polynomial deduced in the oriented case by A. Champanerkar et al. and in the more general unoriented case by E. Dewey and F. Vignes-Tourneret. The generalized Krushkal polynomial also contains the Las Vergnas polynomial of a cellulation of a surface as a specialization; we use this fact to deduce a quasi-tree expansion for the Las Vergnas polynomial.

Original language | English (US) |
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Pages (from-to) | 3-22 |

Number of pages | 20 |

Journal | Advances in Applied Mathematics |

Volume | 94 |

DOIs | |

State | Published - Mar 2018 |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics

## Keywords

- Partial duality
- Quasi-trees
- Ribbon graph polynomials