Geodesic
Binomial edge ideals with quadratic Gröbner bases
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We prove that a binomial edge ideal of a graph $G$ has a quadratic Gröbner basis with respect to some term order if and only if the graph $G$ is closed with respect to a given labelling of the vertices. We also state some criteria for the closedness of a graph $G$ that do not depend on the labelling of its vertex set.
DOI : 10.37236/698
Classification : 13P10, 13C05, 05C25, 13P25, 05E45
Mots-clés : binomial ideal, edge ideal, Gröbner basis 
@article{10_37236_698,
     author = {Marilena Crupi and Giancarlo Rinaldo},
     title = {Binomial edge ideals with quadratic {Gr\"obner} bases},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/698},
     zbl = {1235.13024},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/698/}
}
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Marilena Crupi; Giancarlo Rinaldo. Binomial edge ideals with quadratic Gröbner bases. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/698

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