Regularity and Gröbner bases of the Rees algebra of edge ideals of bipartite graphs

2018/01/20 by Yairon Cid‐Ruiz, Cid-Ruiz, Yairon
Computer Science · Mathematics · #05E40 #13A30 #13D02 #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1801.06731

openalex publication_date 2018/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a bipartite graph and I=I(G) be its edge ideal. The aim of this note is to investigate different aspects of the Rees algebra R(I) of I. We compute its regularity and the universal Gröbner basis of its defining equations; interestingly, both of them are described in terms of the combinatorics of G. We apply these ideas to study the regularity of the powers of I. For any s ≥ match(G)+| E(G) | +1 we prove that reg(I^s+1)=reg(I^s)+2.

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