Isomorphism of Weighted Trees and Stanley's Conjecture for Caterpillars
Combinatorics
2018-06-14 v4
Abstract
This paper contributes to a programme initiated by the first author: `How much information about a graph is revealed in its Potts partition function?'. We show that the -polynomial distinguishes non-isomorphic weighted trees of a \emph{good} family. The framework developed to do so also allows us to show that the -polynomial distinguishes non-isomorphic caterpillars. This establishes Stanley's isomorphism conjecture for caterpillars, an extensively studied problem.
Keywords
Cite
@article{arxiv.1405.4132,
title = {Isomorphism of Weighted Trees and Stanley's Conjecture for Caterpillars},
author = {Martin Loebl and Jean-Sébastien Sereni},
journal= {arXiv preprint arXiv:1405.4132},
year = {2018}
}