The famine was induced, in large part, to rid the Soviet Union of the capitalist Ukrainians (in other words, to force the farmers to give up their land). Though the farmers were able to produce plenty of grain to feed themselves, the government siezed most of what had been harvested.
My great grandparents all left before this time, though most of their relatives stayed behind. Some were sent to Siberia and barely survived. (They had to join the Communist Party or remain outcast.)
Thanks to Katya for the link.
Hmmm, while looking for the photo I also found this page on the famine.