A few more trees the chromatic symmetric function can distinguish

Huryn, Jake; Chmutov, Sergei

doi:10.2140/involve.2020.13.109

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A few more trees the chromatic symmetric function can distinguish

Jake Huryn and Sergei Chmutov

Vol. 13 (2020), No. 1, 109–116

DOI: 10.2140/involve.2020.13.109

Abstract

A well-known open problem in graph theory asks whether Stanley’s chromatic symmetric function, a generalization of the chromatic polynomial of a graph, distinguishes between any two nonisomorphic trees. Previous work has proven the conjecture for a class of trees called spiders. This paper generalizes the class of spiders to $n$ -spiders, where normal spiders correspond to $n = 1$ , and verifies the conjecture for $n = 2$ .

Keywords

graph theory, combinatorics, chromatic symmetric function

Mathematical Subject Classification 2010

Primary: 05C05, 05C31, 05E05

Milestones

Received: 30 March 2019

Revised: 2 August 2019

Accepted: 4 November 2019

Published: 4 February 2020

Communicated by Joel Foisy

Authors

Jake Huryn
The Ohio State University Columbus, OH United States

Sergei Chmutov
The Ohio State University Columbus, OH United States

Vol. 13, No. 1, 2020