The arithmetical rank of the edge ideals of graphs with pairwise disjoint cycles

TL;DR

This paper establishes an upper bound on the arithmetical rank of edge ideals for graphs with disjoint cycles, linking algebraic properties to graph structure.

Contribution

It provides a new bound on the arithmetical rank of edge ideals for graphs with pairwise disjoint cycles, connecting combinatorial and algebraic invariants.

Findings

Arithmetical rank is bounded above by the sum of the number of cycles and the maximum height of associated primes.

The result applies specifically to graphs with pairwise vertex-disjoint cycles.

The bound improves understanding of the algebraic complexity of such graph ideals.

Abstract

We prove that, for the edge ideal of a graph whose cycles are pairwise vertex-disjoint, the arithmetical rank is bounded above by the sum of the number of cycles and the maximum height of its associated primes.