Critical subgraphs and the regularity of symbolic powers of cover ideals of graphs

TL;DR

This paper introduces a method leveraging t-admissible subgraphs to compute the regularity of symbolic powers of cover ideals in graphs, with specific results for bipartite unicyclic graphs.

Contribution

It presents a novel approach for determining the regularity of symbolic powers of cover ideals using t-admissible subgraphs, applied to bipartite unicyclic graphs.

Findings

Method for using t-admissible subgraphs to determine regularity

Computed regularity of powers of cover ideals for bipartite unicyclic graphs

Provides a new tool for analyzing symbolic powers in graph theory

Abstract

Let $G$ be a simple graph. We demonstrate a method for using $t$-admissible subgraphs of $G$ to determine the regularity of the $t$-th symbolic power of the cover ideal of $G$. As an application, we compute the regularity of powers of cover ideals of bipartite unicyclic graphs.