Journal of Algebraic Combinatorics

, Volume 44, Issue 1, pp 99–117

Parity binomial edge ideals


DOI: 10.1007/s10801-015-0657-3

Cite this article as:
Kahle, T., Sarmiento, C. & Windisch, T. J Algebr Comb (2016) 44: 99. doi:10.1007/s10801-015-0657-3


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 and 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.


Binomial ideals Primary decomposition Mesoprimary decomposition Binomial edge ideals Markov bases 

Mathematics Subject Classification

Primary 05E40 Secondary 13P10 05C38 

Funding information

Funder NameGrant NumberFunding Note
Studienstiftung des Deutschen Volkes
  • Award-ID

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Thomas Kahle
    • 1
  • Camilo Sarmiento
    • 1
  • Tobias Windisch
    • 1
  1. 1.Otto-von-Guericke Universität MagdeburgMagdeburgGermany

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