Ideal quotients of edge ideals and minimal vertex covers
Location
Bent Corridor, Science Center
Document Type
Poster - Open Access
Start Date
5-1-2026 12:00 PM
End Date
5-1-2026 2:00 PM
Abstract
Certain properties of simple graphs are known to reveal information about edge ideals produced by those graphs, and vice versa. For example, work by Fröberg and Herzog, Hibi, and Zheng shows that the edge ideal of a graph has a linear quotient ordering if and only if the complement of that graph is chordal. This research explores the connections between the edge ideals and vertex covers of simple graphs. Building on a proof about cover ideals of graphs by Van Tuyl, we show that the quotients of the edge ideal of a simple graph G correspond to vertices in a minimal vertex cover of a graph formed by removing exactly one edge from G.
Keywords:
DG algebra, Edge ideal, Graph theory
Recommended Citation
Wang, Reed, "Ideal quotients of edge ideals and minimal vertex covers" (2026). Research Symposium. 21.
https://digitalcommons.oberlin.edu/researchsymp/2026/posters/21
Major
Math; Computer Science; Musical Studies
Project Mentor(s)
Rachel Diethorn, Mathematics
2026
Ideal quotients of edge ideals and minimal vertex covers
Bent Corridor, Science Center
Certain properties of simple graphs are known to reveal information about edge ideals produced by those graphs, and vice versa. For example, work by Fröberg and Herzog, Hibi, and Zheng shows that the edge ideal of a graph has a linear quotient ordering if and only if the complement of that graph is chordal. This research explores the connections between the edge ideals and vertex covers of simple graphs. Building on a proof about cover ideals of graphs by Van Tuyl, we show that the quotients of the edge ideal of a simple graph G correspond to vertices in a minimal vertex cover of a graph formed by removing exactly one edge from G.
