No Embedding Found Error on Structural Frustration example

I am going through the Structural Imbalance demo, here, and I wanted to know how big of a problem could be solved simply by increasing the size of the graph. In the example, we start with a 4-node fully connected graph. Increasing the graph size up to 65 nodes, takes less than 5 seconds to solve,

However, the script runs into a "No Embedding Found" error when I reach 66 nodes,

Why is that? My first guess is that a fully connected, 66-node graph contains too many parameters to be implemented onto the 2000 qubits chip, and there exists no embedding that can map this problem onto the chip. But I am not sure if this is correct, and having the correct explanation would be very much welcome.



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