We show that the universal Gröbner basis and the Graver basis of a binomial edge ideal coincide. We provide a description for this basis set in terms of certain paths in the underlying graph. We conjecture a similar result for a parity binomial edge ideal and prove this conjecture for the case when the underlying graph is the complete graph.
@article{10_37236_5912,
author = {Mourtadha Badiane and Isaac Burke and Emil Sk\"oldberg},
title = {The universal {Gr\"obner} basis of a binomial edge ideal},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {4},
doi = {10.37236/5912},
zbl = {1442.13088},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5912/}
}
TY - JOUR
AU - Mourtadha Badiane
AU - Isaac Burke
AU - Emil Sköldberg
TI - The universal Gröbner basis of a binomial edge ideal
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5912/
DO - 10.37236/5912
ID - 10_37236_5912
ER -
%0 Journal Article
%A Mourtadha Badiane
%A Isaac Burke
%A Emil Sköldberg
%T The universal Gröbner basis of a binomial edge ideal
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5912/
%R 10.37236/5912
%F 10_37236_5912
Mourtadha Badiane; Isaac Burke; Emil Sköldberg. The universal Gröbner basis of a binomial edge ideal. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/5912
