arXiv subjects

Keri Ann Sather-Wagstaff

Publications and source records attributed to Keri Ann Sather-Wagstaff.

5 recordsLinked to original sources

arXiv2026

Characterization of Well-Totally Dominated Trees

Let $G$ be a graph with no isolated vertices. A set of vertices $S$ is a total dominating set (TDS) if every vertex in $G$ is adjacent to at least one vertex in $S$. We say $G$ is well-totally dominated (WTD) if every minimal TDS has the same size. In this paper, we present two characterizations of well-totally dominated trees, one being descriptive and the other being constructive. In particular, our characterizations imply that it takes only polynomial time to verify whether a given tree is WTD.

math.CO↗

arXiv2026

Open Neighborhood Ideals of Well-Totally Dominated Trees are Cohen-Macaulay

We introduce and investigate the open neighborhood ideal $\mathcal{N}(G)$ of a finite simple graph $G$. We describe the minimal primary decomposition of $\mathcal{N}(G)$ in terms of the minimal total dominating sets (TDSs) of $G$. Then we prove that the open neighborhood ideal of a tree is Cohen-Macaulay if and only if the tree is well-totally dominated (WTD) and calculate the Cohen-Macaulay type.

math.AC↗

arXiv2025

André-Quillen homology and ascent of complete intersection flat dimensions

Using André-Quillen homology, we prove an ascent result for different types of complete intersection flat dimensions along an essentially of finite type flat local homomorphism with complete intersection closed fiber. As an application of our result, we extend a result of Majadas Soto and of Avramov, Henriques and Şega on the André-Quillen dimension of surjective local homomorphisms to that of essentially of finite types.

math.AC↗

arXiv2024

Minimal Free Resolutions of Edge Ideals of Edge-Weighted Complete Bipartite Graphs

We explicitly describe cellular minimal free resolutions of certain classes of edge ideals of weighted complete bipartite graphs based on a construction of Visscher. Specifically, we show that Visscher's construction minimally resolves all edge ideals of undirected vertex-weighted complete bipartite graphs, and we characterize the edge-weighted complete bipartite graphs whose edge ideals are minimally resolved by Visscher's construction.

math.AC↗

arXiv2023

Ring homomorphisms and local rings with quasi-decomposable maximal ideal

The notion of local rings with quasi-decomposable maximal ideal was formally introduced by Nasseh and Takahashi. In separate works, the authors of the present paper show that such rings have rigid homological properties; for instance, they are both Ext- and Tor-friendly. One point of this paper is to further explore the homological properties of these rings and also introduce new classes of such rings from a combinatorial point of view. Another point is to investigate how far some of these homological properties can be pushed along certain diagrams of local ring homomorphisms.

math.AC↗