@article{79ea0be2dc0f48ec955516957c705e19,
title = "On the smallest trees with the same restricted U-polynomial and the rooted U-polynomial",
abstract = "In this article, we construct explicit examples of pairs of non-isomorphic trees with the same restricted U-polynomial for every k; by this we mean that the polynomials agree on terms with degree at most k+1. The main tool for this construction is a generalization of the U-polynomial to rooted graphs, which we introduce and study in this article. Most notably we show that rooted trees can be reconstructed from its rooted U-polynomial.",
keywords = "chromatic symmetric function, graph polynomials, rooted trees, tree distinguishing conjecture",
author = "Jos{\'e} Aliste-Prieto and {de Mier}, Anna and Jos{\'e} Zamora",
note = "Funding Information: The authors would like to thank the referees for many suggestions that improved the presentation of this paper. The first and third author are partially supported by CONICYT FONDECYT Regular, Chile 1160975 and Basal PFB-03 CMM Universidad de Chile . The second author is partially supported by the Spanish Ministerio de Econom{\'i}a y Competitividad, Spain project MTM2017-82166-P . A short version of this work appeared in [3] . Publisher Copyright: {\textcopyright} 2020 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2021",
month = mar,
doi = "10.1016/j.disc.2020.112255",
language = "English",
volume = "344",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "3",
}