Let $I(G)^{[k]}$ denote the $k$th squarefree power of the edge ideal of $G$. When $G$ is a forest, we provide a sharp upper bound for the regularity of $I(G)^{[k]}$ in terms of the $k$-admissable matching number of $G$. For any positive integer $k$, we classify all forests $G$ such that $I(G)^{[k]}$ has linear resolution. We also give a combinatorial formula for the regularity of $I(G)^{[2]}$ for any forest $G$.
@article{10_37236_10038,
author = {Nursel Erey and Takayuki Hibi},
title = {Squarefree powers of edge ideals of forests},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {2},
doi = {10.37236/10038},
zbl = {1465.13018},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10038/}
}
TY - JOUR
AU - Nursel Erey
AU - Takayuki Hibi
TI - Squarefree powers of edge ideals of forests
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/10038/
DO - 10.37236/10038
ID - 10_37236_10038
ER -
%0 Journal Article
%A Nursel Erey
%A Takayuki Hibi
%T Squarefree powers of edge ideals of forests
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/10038/
%R 10.37236/10038
%F 10_37236_10038
Nursel Erey; Takayuki Hibi. Squarefree powers of edge ideals of forests. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/10038
