1 3 M ay 2 00 8 Cut ideals of K 4-minor free graphs are generated by quadrics

@inproceedings{Engstrm200813M,
title={1 3 M ay 2 00 8 Cut ideals of K 4-minor free graphs are generated by quadrics},
author={Alexander Engstr{\"o}m},
year={2008}
}

Cut ideals of K 4-minor free graphs are generated by quadrics. Abstract We prove a conjecture by Sturmfels and Sullivant, that the cut ideal is generated by quadrics if and only if the graph is free of K4 minors. It is a corollary of a fiber product type theorem with which one can glue together graphs in two non-adjacent vertices and get generators for the cut ideal.