The arithmetical rank of the edge ideals of graphs with whiskers

TL;DR

This paper proves that for certain classes of graphs with whiskers and other squarefree monomial ideals, the arithmetical rank equals the big height, advancing understanding of their algebraic properties.

Contribution

It establishes the equality of arithmetical rank and big height for graphs with whiskers and extends this result to broader classes of squarefree monomial ideals.

Findings

Arithmetical rank equals big height for graphs with whiskers.

Extension of results to other classes of squarefree monomial ideals.

Provides algebraic insights into the structure of these ideals.

Abstract

We consider the edge ideals of large classes of graphs with whiskers and for these ideals we prove that the arithmetical rank is equal to the big height. Then we extend these results to other classes of squarefree monomial ideals, generated in any degree, proving that the same equality holds.