A recurrence for certain Tutte polynomials

Vincent Brugidou

A recurrence for certain Tutte polynomials

Combinatorics 2025-11-19 v2

Authors: Vincent Brugidou

Abstract

We combinatorially prove a new recurrence between the Tutte polynomials of graphs obtained by contraction of the complete graphs $K_{n}$ %. This generalizes, to two variables, a relation previously obtained by the author between the inversion enumerator polynomials in the colored tree sequences.

Keywords

graph polynomials combinatorics kazhdan-lusztig polynomials

Cite

@article{arxiv.2509.20959,
  title  = {A recurrence for certain Tutte polynomials},
  author = {Vincent Brugidou},
  journal= {arXiv preprint arXiv:2509.20959},
  year   = {2025}
}

Comments

9 pages, 3 figures. Everything related to the conjecture in version 1 has been removed because it turned out to be false

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