Let $I=I(D)$ be the edge ideal of a weighted oriented graph $D$ whose underlying graph is $G$. We determine the irredundant irreducible decomposition of $I$. Also, we characterize the associated primes and the unmixed property of $I$. Furthermore, we give a combinatorial characterization for the unmixed property of $I$, when $G$ is bipartite, $G$ is a graph with whiskers or $G$ is a cycle. Finally, we study the Cohen–Macaulay property of $I$.
@article{10_37236_8479,
author = {Yuriko Pitones and Enrique Reyes and Jonathan Toledo},
title = {Monomial ideals of weighted oriented graphs},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8479},
zbl = {1419.05099},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8479/}
}
TY - JOUR
AU - Yuriko Pitones
AU - Enrique Reyes
AU - Jonathan Toledo
TI - Monomial ideals of weighted oriented graphs
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8479/
DO - 10.37236/8479
ID - 10_37236_8479
ER -
%0 Journal Article
%A Yuriko Pitones
%A Enrique Reyes
%A Jonathan Toledo
%T Monomial ideals of weighted oriented graphs
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8479/
%R 10.37236/8479
%F 10_37236_8479
Yuriko Pitones; Enrique Reyes; Jonathan Toledo. Monomial ideals of weighted oriented graphs. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8479
