Binomial edge ideals of crown graphs

2025/07/05 by Arvind Kumar, Kumar, Arvind, Joshua Pomeroy +3
Computer Science · Mathematics · #05E40 #13C10 #13C15 #13F20 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.03889

openalex publication_date 2025/07/05 · openalex created_date 2025/10/20 · openalex updated_date 2026/07/28

Abstract

In this article, we explore the class of graphs for which the projective dimension of the quotient of the binomial edge ideals matches the big height of that ideal. Additionally, we investigate the Vasconcelos number of binomial edge ideals for cycles and crown graphs. We also provide proof for [Conjecture 4.13, 3], which is related to the Vasconcelos number of binomial edge ideals for cycles.

Citations

• The v-Number of Binomial Edge Ideals
• Connected domination in graphs and v-numbers of binomial edge ideals
• Binomial expansion for saturated and symbolic powers of sums of ideals
• On the depth of binomial edge ideals of graphs
• Binomial edge ideals of small depth
• Depth and Extremal Betti Number of Binomial Edge Ideals
• Some Cohen-Macaulay and unmixed binomial edge ideals
• On the Betti numbers of some classes of Binomial edge ideals
• Cohen-Macaulay binomial edge ideals
• Graphs and Ideals generated by some 2-minors
• Binomial edge ideals and conditional independence statements

Cited by

• The V-Number of Binomial Edge Ideals: Minimal Cuts and Cycle Graphs

Related

• On binomial edge ideals of corona of graphs
• On the v-number of binomial edge ideals of some classes of graphs
• Binomial Edge Ideals of Complements of Graphs of Girth at Least 5
• Binomial edge ideals of cographs
• Binomial edge ideals with pure resolutions