Certain Homological Invariants of Bipartite Kneser Graphs

TL;DR

This paper derives combinatorial formulas for Betti numbers, bounds on regularity and projective dimension of edge ideals in bipartite Kneser graphs, linking algebraic invariants to combinatorial properties.

Contribution

It provides new combinatorial formulas and bounds for algebraic invariants of edge ideals of bipartite Kneser graphs, advancing understanding of their homological properties.

Findings

Betti numbers computed via combinatorial formulas

Bounds established for regularity of powers of edge ideals

Bounds derived for projective dimension based on combinatorial data

Abstract

In this paper, we obtain a combinatorial formula for computing the Betti numbers in the linear strand of edge ideals of bipartite Kneser graphs. We deduce lower and upper bounds for regularity of powers of edge ideals of these graphs in terms of associated combinatorial data and show that the lower bound is attained in some cases. Also, we obtain bounds on the projective dimension of edge ideals of these graphs in terms of combinatorial data.