Parity binomial edge ideals

Abstract

Parity binomial edge ideals of simple undirected graphs are introduced. Unlike binomial edge ideals, they do not have square-free Gröbner bases and are radical if only if the graph is bipartite or the characteristic of the ground field is not two. The minimal primes are determined and shown to encode combinatorics of even and odd walks in the graph. A mesoprimary decomposition is determined and shown to be a primary decomposition in characteristic two.

21 pages, 3 figures, v2: minor problem in proof of Lemma 2.4 corrected, construction of Gröbner basis in Section 3 corrected, Example 5.1 replaced by Remark 5.1, final version as in Journal of Algebraic Combinatorics, v3: footnote to Lemma 3.8 added

References in corpus (2)

• Detecting Binomiality
• On the ideal of orthogonal representations of a graph in ${\mathbb{R}}^2$

Cited by in corpus (9)

• Regularity of powers of quadratic sequences with applications to binomial ideals
• Lovász-Saks-Schrijver ideals and parity binomial edge ideals of graphs
• Cohen-Macaulay binomial edge ideals and accessible graphs
• Regularity of powers of d-sequence (parity) binomial edge ideals of unicycle graphs
• Hilbert-Poincaré series of parity binomial edge ideals and permanental ideals of complete graph
• F-Purity of Binomial Edge Ideals
• Parity Binomial Edge Ideals with Pure Resolutions
• Comparison of symbolic and ordinary powers of parity binomial edge ideals
• Classification of unmixed parity binomial edge ideals of cactus and chordal graphs