Motivated by Stanley and Stembridge's conjecture about the $e$-positivity of claw-free incomparability graphs, Hamel and her collaborators 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, Hoáng and Tuero, and another problem considered by Foley, Hoáng and Merkel.
@article{10_37236_9910,
author = {Grace M. X. Li and Arthur L. B. Yang},
title = {On the \(e\)-positivity of \((claw, {2K_2)\)-free} graphs},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {2},
doi = {10.37236/9910},
zbl = {1466.05220},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9910/}
}
TY - JOUR
AU - Grace M. X. Li
AU - Arthur L. B. Yang
TI - On the \(e\)-positivity of \((claw, 2K_2)\)-free graphs
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/9910/
DO - 10.37236/9910
ID - 10_37236_9910
ER -
%0 Journal Article
%A Grace M. X. Li
%A Arthur L. B. Yang
%T On the \(e\)-positivity of \((claw, 2K_2)\)-free graphs
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/9910/
%R 10.37236/9910
%F 10_37236_9910
Grace M. X. Li; Arthur L. B. Yang. On the \(e\)-positivity of \((claw, 2K_2)\)-free graphs. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9910
