Regularity of Powers of Bipartite Graphs
A V Jayanthan, N Narayanan, S Selvaraja

TL;DR
This paper investigates the regularity of powers of edge ideals in bipartite graphs, providing upper bounds, comparisons with associated graphs, and explicit calculations for specific subclasses, advancing understanding of algebraic properties of bipartite graphs.
Contribution
It introduces new upper bounds for the regularity of powers of edge ideals in bipartite graphs and compares properties of related graphs to facilitate explicit calculations.
Findings
Established upper bounds for reg$(I(G)^s)$ in bipartite graphs.
Compared properties of $G$ and $G'$ related to polarization and colon ideals.
Explicitly computed reg$(I(G)^s)$ for certain subclasses of bipartite graphs.
Abstract
Let be a finite simple graph and denote the corresponding edge ideal. For all , we obtain upper bounds for reg for bipartite graphs. We then compare the properties of and , where is the graph associated with the polarization of the ideal , where are edges of . Using these results, we explicitly compute reg for several subclasses of bipartite graphs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph theory and applications · Finite Group Theory Research · Advanced Graph Theory Research
