Sazdanovic and Yip (2018) defined a categorification of Stanley's chromatic sym-metric function called the chromatic symmetric homology, given by a suitable family of representations of the symmetric group. In this paper we prove that, as conjec-tured by Chandler, Sazdanovic, Stella and Yip (2019), if a graph G is non-planar, then its chromatic symmetric homology in bidegree (1,0) contains Z2-torsion. Our proof follows a recursive argument based on Kuratowsky's theorem.
On Chromatic Symmetric Homology and Planarity of Graphs / Ciliberti, Azzurra; Moci, Luca. - In: ELECTRONIC JOURNAL OF COMBINATORICS. - ISSN 1077-8926. - 30:1(2023), pp. 1-11. [10.37236/11397]
On Chromatic Symmetric Homology and Planarity of Graphs
Azzurra Ciliberti
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2023
Abstract
Sazdanovic and Yip (2018) defined a categorification of Stanley's chromatic sym-metric function called the chromatic symmetric homology, given by a suitable family of representations of the symmetric group. In this paper we prove that, as conjec-tured by Chandler, Sazdanovic, Stella and Yip (2019), if a graph G is non-planar, then its chromatic symmetric homology in bidegree (1,0) contains Z2-torsion. Our proof follows a recursive argument based on Kuratowsky's theorem.| File | Dimensione | Formato | |
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