Around matrix-tree theorem

Yurii Burman; Boris Shapiro

Around matrix-tree theorem

Combinatorics 2007-05-23 v2

Authors: Yurii Burman , Boris Shapiro

Abstract

Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system $D_n$ (the classical theorem corresponds to the $A_n$ -case). Several byproducts of the developed technique, such as a new formula for a specialization of the multivariate Tutte polynomial, are of independent interest.

Keywords

phylogenetic trees spanning trees graph polynomials

Cite

@article{arxiv.math/0512164,
  title  = {Around matrix-tree theorem},
  author = {Yurii Burman and Boris Shapiro},
  journal= {arXiv preprint arXiv:math/0512164},
  year   = {2007}
}

Comments

13 pages, no figures

Around matrix-tree theorem

Abstract

Keywords

Cite

Comments

Related papers