For any two integers $d,r \geqslant 1$, we show that there exists an edge ideal $I(G)$ such that ${\rm reg}\left(R/I(G)\right)$, the Castelnuovo-Mumford regularity of $R/I(G)$, is $r$, and $\deg h_{R/I(G)}(t)$, the degree of the $h$-polynomial of $R/I(G)$, is $d$. Additionally, if $G$ is a graph on $n$ vertices, we show that ${\rm reg}\left(R/I(G)\right) + \deg h_{R/I(G)}(t) \leqslant n$.
@article{10_37236_8247,
author = {Takayuki Hibi and Kazunori Matsuda and Adam Van Tuyl},
title = {Regularity and \(h\)-polynomials of edge ideals},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {1},
doi = {10.37236/8247},
zbl = {1440.13060},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8247/}
}
TY - JOUR
AU - Takayuki Hibi
AU - Kazunori Matsuda
AU - Adam Van Tuyl
TI - Regularity and \(h\)-polynomials of edge ideals
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8247/
DO - 10.37236/8247
ID - 10_37236_8247
ER -
%0 Journal Article
%A Takayuki Hibi
%A Kazunori Matsuda
%A Adam Van Tuyl
%T Regularity and \(h\)-polynomials of edge ideals
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8247/
%R 10.37236/8247
%F 10_37236_8247
Takayuki Hibi; Kazunori Matsuda; Adam Van Tuyl. Regularity and \(h\)-polynomials of edge ideals. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/8247
