The monomial ideal of independent sets associated to a graph
Commutative Algebra
2013-07-12 v1 Combinatorics
Abstract
Independent sets play a key role into the study of graphs and important problems arising in graph theory reduce to them. We define the monomial ideal of independent sets associated to a finite simple graph and describe its homological and algebraic invariants in terms of the combinatorics of the graph. We compute the minimal primary decomposition and characterize the Cohen--Macaulay ideals. Moreover, we provide a formula for computing the Betti numbers, which depends only on the coefficients of the independence polynomial of the graph.
Keywords
Cite
@article{arxiv.1307.3050,
title = {The monomial ideal of independent sets associated to a graph},
author = {Oana Olteanu},
journal= {arXiv preprint arXiv:1307.3050},
year = {2013}
}