Sazdanovic and Yip (2018) defined a categorification of Stanley’s chromatic symmetric function called the chromatic symmetric homology, given by a suitable family of representations of the symmetric group. In this paper we prove that, as conjectured by Chandler, Sazdanovic, Stella and Yip (2019), 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.
@article{10_37236_11397,
author = {Azzurra Ciliberti and Luca Moci},
title = {On chromatic symmetric homology and planarity of graphs},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {1},
doi = {10.37236/11397},
zbl = {1507.05099},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11397/}
}
TY - JOUR
AU - Azzurra Ciliberti
AU - Luca Moci
TI - On chromatic symmetric homology and planarity of graphs
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/11397/
DO - 10.37236/11397
ID - 10_37236_11397
ER -
%0 Journal Article
%A Azzurra Ciliberti
%A Luca Moci
%T On chromatic symmetric homology and planarity of graphs
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/11397/
%R 10.37236/11397
%F 10_37236_11397
Azzurra Ciliberti; Luca Moci. On chromatic symmetric homology and planarity of graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11397
