Graph Connectivity and Binomial Edge Ideals

2016/05/01 by Banerjee, Arindam, Núñez-Betancourt, Luis · 1 citation
#05C40 #05E40 #13C14 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.00314

Abstract

We relate homological properties of a binomial edge ideal J_G to invariants that measure the connectivity of a simple graph G. Specifically, we show if R/J_G is a Cohen-Macaulay ring, then graph toughness of G is exactly (1)/(2). We also give an inequality between the depth of R/J_G and the vertex-connectivity of G. In addition, we study the Hilbert-Samuel multiplicity, and the Hilbert-Kunz multiplicity of R/J_G.

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• Binomial edge ideals of Cameron-Walker graphs

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