Geodesic
Divisors on graphs, Connected flags, and Syzygies
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gröbner theory. We give an explicit description of a minimal Gröbner basis for each higher syzygy module. In each case the given minimal Gröbner basis is also a minimal generating set. The Betti numbers of $I_G$ and its initial ideal (with respect to a natural term order) coincide and they correspond to the number of ``connected flags'' in $G$. Moreover, the Betti numbers are independent of the characteristic of the base field. 
@article{DMTCS_2013_special_264_a35,
     author = {Mohammadi, Fatemeh and Shokrieh, Farbod},
     title = {Divisors on graphs, {Connected} flags, and {Syzygies}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.2351},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2351/}
}
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%J Discrete mathematics & theoretical computer science
%D 2013
%V DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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Mohammadi, Fatemeh; Shokrieh, Farbod. Divisors on graphs, Connected flags, and Syzygies. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.2351. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2351/

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