Geodesic
On complete intersection toric ideals of graphs
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 351-370.

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Summary: We study the graphs G for which their toric ideals I $_{ G }$ are complete intersections. In particular, we prove that for a connected graph G such that I $_{ G }$ is a complete intersection all of its blocks are bipartite except for at most two. We prove that toric ideals of graphs which are complete intersections are circuit ideals. In this case, the generators of the toric ideal correspond to even cycles of G except of at most one generator, which corresponds to two edge disjoint odd cycles joint at a vertex or with a path. We prove that the blocks of these graphs satisfy the odd cycle condition. Finally, we characterize all complete intersection toric ideals of graphs which are normal.
Keywords: complete intersections, graphs, toric ideals 
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     author = {Tatakis, Christos and Thoma, Apostolos},
     title = {On complete intersection toric ideals of graphs},
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     pages = {351--370},
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     number = {2},
     year = {2013},
     language = {en},
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Tatakis, Christos; Thoma, Apostolos. On complete intersection toric ideals of graphs. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 351-370. http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a6/