Cut ideals of K4-minor free graphs are generated by quadrics

Details Cut ideals of K4-minor free graphs are generated by quadrics Cut ideals of K4-minor free graphs are generated by quadrics

2008-05-13

arxiv.org/abs/0805.1762v3

Mathematics

Commutative Algebra

Revised version. Extended introduction and minor changes. 11 pages

Scientific paper

Cut ideals are used in algebraic statistics to study statistical models defined by graphs. Intuitively, topological restrictions on the graphs should imply structural statements about the corresponding cut ideals. Several theorems and many computer calculations support that. Sturmfels and Sullivant conjectured that the cut ideal is generated by quadrics if and only if the graph is free of K4-minors. Parts of the conjecture has been resolved by Brennan and Chen, and later by Nagel and Petrovic. We prove the full conjecture by introducing a new type of toric fiber product theorem.

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