Nonvanishing Betti Numbers of Weakly Chordal Graphs

TL;DR

This paper extends a known condition for non-vanishing multigraded Betti numbers from chordal graphs to the broader class of weakly chordal graphs, enhancing understanding of their algebraic properties.

Contribution

It generalizes Kimura's condition, providing a new criterion applicable to weakly chordal graphs for the non-vanishing of Betti numbers.

Findings

Kimura's condition applies to weakly chordal graphs

Extended the characterization of Betti number non-vanishing

Broadened the class of graphs with known Betti number behavior

Abstract

We show that Kimura's necessary and sufficient condition for the non-vanishingness of multigraded Betti numbers of chordal graphs can be extended to the wider class of weakly chordal graphs.