On chromatic symmetric homology and planarity of graphs

Abstract

Sazdanovic and Yip defined a categorification of Stanley's chromatic function called the chromatic symmetric homology. In this paper we prove that (as conjectured by Chandler, Sazdanovic, Stella and Yip), if a graph $G$ is non-planar, then its chromatic symmetric homology in bidegree (1,0) contains ${\mathbb{Z}}_2$-torsion. Our proof follows a recursive argument based on Kuratowsky's theorem.

11 pages. Some changes have been made in Section 3 in order to improve readability. arXiv admin note: substantial text overlap with arXiv:1911.13297 by other authors

References in corpus (1)

• On the Strength of Chromatic Symmetric Homology for graphs

Cited by in corpus (1)

• A deletion-contraction long exact sequence for chromatic symmetric homology