Geometric vertex decomposition and liaison for toric ideals of graphs
The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic
generalization of the vertex decomposability property for simplicial complexes. Indeed, a …
generalization of the vertex decomposability property for simplicial complexes. Indeed, a …
Three invariants of geometrically vertex decomposable ideals
We study three invariants of geometrically vertex decomposable ideals: the Castelnuovo-
Mumford regularity, the multiplicity, and the $ a $-invariant. We show that these invariants …
Mumford regularity, the multiplicity, and the $ a $-invariant. We show that these invariants …
Comparability of the total Betti numbers of toric ideals of graphs
G Favacchio - arXiv preprint arXiv:2404.17836, 2024 - arxiv.org
The total Betti numbers of the toric ideal of a simple graph are, in general, highly sensitive to
any small change of the graph. In this paper we look at some combinatorial operations that …
any small change of the graph. In this paper we look at some combinatorial operations that …
ON BASIC DOUBLE G-LINKS OF SQUAREFREE MONOMIAL IDEALS
P Klein, M Koban, J Rajchgot - Journal of Commutative Algebra, 2024 - projecteuclid.org
Nagel and Römer introduced the class of weakly vertex decomposable simplicial
complexes, which include matroid, shifted, and Gorenstein complexes as well as vertex …
complexes, which include matroid, shifted, and Gorenstein complexes as well as vertex …
Exploring Graph-Theoretic Properties Using Geometric Vertex Decomposition
A Czerniak-Nachman - 2023 - search.proquest.com
Geometric vertex decomposition can be a useful tool in algebraic graph theory for studying
properties of graphs. For any finite simple graph G, we can define an algebraic structure …
properties of graphs. For any finite simple graph G, we can define an algebraic structure …