Stanley depth of edge ideals

TL;DR

This paper establishes upper bounds for the Stanley depth of edge ideals in certain hypergraphs and confirms Stanley's conjecture for these cases, advancing understanding of algebraic properties of hypergraph edge ideals.

Contribution

It provides new upper bounds for Stanley depth of edge ideals in k-partite complete graphs and k-uniform complete bipartite hypergraphs, and verifies Stanley's conjecture for these cases.

Findings

Stanley's conjecture holds for the considered edge ideals.

Upper bounds are established for the Stanley depth in specific hypergraph classes.

Results contribute to the algebraic understanding of hypergraph edge ideals.

Abstract

We give an upper bound for the Stanley depth of the edge ideal $I$ of a $k$-partite complete graph and show that Stanley's conjecture holds for $I$. Also we give an upper bound for the Stanley depth of the edge ideal of a $k$-uniform complete bipartite hypergraph.