A Note on Distinguishing Trees with the Chromatic Symmetric Function

2021/06/08 by Crew, Logan · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.04417

Abstract

For a tree T, consider its smallest subtree T^∘ containing all vertices of degree at least 3. Then the remaining edges of T lie on disjoint paths each with one endpoint on T^∘. We show that the chromatic symmetric function of T determines the size of T^∘, and the multiset of the lengths of these incident paths. In particular, this generalizes a proof of Martin, Morin, and Wagner that the chromatic symmetric function distinguishes spiders.

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• Chromatic MacMahon symmetric functions of graphs

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