Well, technically, there is no lower size limit. By all means use 1x1 if you think you can give enough support!
However, I think what you really mean is, can you use 4x2 or 6x2 timber for the frame? If that IS your question, then the answer is yes you can use 4x2 so long as it is well supported. If budget allows though, I'd always opt for 6x2 if you can handle the extra 2" of height that would give ya.
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