Cluster-variable connectivity conjecture

A cluster variable is a variable occurring in a cluster, a seed is a cluster together with its exchange data, and the exchange graph is the graph whose vertices are seeds and whose edges correspond to seed mutations. Cluster-variable connectivity conjecture. For any cluster variable $x$, the seeds whose clusters contain $x$ induce a connected subgraph of the exchange graph. This is attributed to Fomin–Zelevinsky and is presented as a conjecture about when two cluster variables can be equal; the source does not state a resolution.