Graded Betti numbers of path ideals of cycles and lines

2011/10/30 by Alilooee, Ali, Faridi, Sara · 3 citations
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1110.6653

Abstract

We use purely combinatorial arguments to give a formula to compute all graded Betti numbers of path ideals of line graphs and cycles. As a consequence we can give new and short proofs for the known formulas of regularity and projective dimensions of path ideals of line graphs.

Cited by

• Scarf complexes of connected and path ideals
• Barile-Macchia Resolutions and the closed neighborhood ideal
• Depth of the 3-path Ideal of Square of a Path

Related

• On the resolution of path ideals of cycles
• Projective dimension and regularity of path ideals of cycles
• Multigraded Betti numbers of some path ideals
• Non-vanishingness of Betti numbers of edge ideals
• Path ideals of rooted trees and their graded Betti numbers