On the \(e\)-positivity of \((claw, 2K_2)\)-free graphs
type: Item
instance of: scholarly article
title: On the \(e\)-positivity of \((claw, 2K_2)\)-free graphs
zbMATH Open document ID: 1466.05220
DOI: 10.37236/9910
author: Yanyan Li
published in: The Electronic Journal of Combinatorics
publication date: 2021-06-21T00:00:00Z
review text: Summary: Motivated by Stanley and Stembridge's conjecture [\textit{R. P. Stanley} and \textit{J. R. Stembridge}, J. Comb. Theory, Ser. A 62, No. 2, 261--279 (1993; Zbl 0772.05097)] about the \(e\)-positivity of claw-free incomparability graphs, Hamel and her collaborators [\textit{A. M. Hamel} et al., Graphs Comb. 35, No. 4, 815--825 (2019; Zbl 1416.05105)] studied the \(e\)-positivity of \((claw, H)\)-free graphs, where \(H\) is a four-vertex graph. In this paper we establish the \(e\)-positivity of generalized pyramid graphs and \(2K_2\)-free unit interval graphs, which are two important families of \((claw, 2K_2)\)-free graphs. Hence we affirmatively solve one problem proposed by Hamel et al. [loc. cit.], and another problem considered by \textit{A. M. Foley} et al. [Electron. J. Comb. 26, No. 3, Research Paper P3.51, 20 p. (2019; Zbl 1420.05177)].
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 7361298
zbMATH Keywords: chromatic symmetric function
zbMATH Keywords: claw-free graphs
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.37236/9910
OpenAlex ID: W3176753413
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description: scientific article; zbMATH DE number 7361298