Binomiality of colored Gaussian graphical models

Colored Gaussian graphical models are linear concentration models in which the entries of the concentration matrices satisfy equalities defined by the coloring and edges of an underlying graph.

Following earlier work by Coons-Maraj-Misra-Sorea and Misra-Sullivant, we study the vanishing ideal of these models and present a necessary and sufficient condition for such a model to have binomial vanishing ideal.

In this talk, I will introduce block graphs and triangle-regular coloring, and we will see why those are necessary conditions for the ideal to be binomial. We will see properties of these graphs and connect them to RCOP graphs and association schemes. In particular, using association schemes without transitive group action, we see that binomiality does not imply that the color classes must be orbits under the automorphism group of the colored graph.

This is based on joint work with Jan Draisma and Magdaléna Mišinová.