Non-adjacent-node merging conjecture for BMT-derived graphs

A BMT-derived graph is a graph obtained from the tree model by merging color classes of edges. Two internal nodes are non-adjacent when they are not joined by an edge in the underlying tree. Non-adjacent merging conjecture. Any BMT-derived graph constructed by merging color classes of edges that correspond to non-adjacent internal nodes is not toric. The conjecture is motivated by computations in which all examples of merging non-adjacent internal nodes produced ideals that were not toric under any linear change of variables; the source does not report a resolution.