Atkins diet = no acne?

I'm a 25 year old male with mild acne. My wife goes on the Atkins diet hardcore, for 1-3 months at a time about twice a year. Needless to say, when she goes on it, so do I. Over the last couple of years I've noticed that my complexion clears up very nicely when we cut out the carbs and the acne comes right back when I start eating a regular (still healthy) diet.

Does anyone know what it is about the Atkins diet that would cause this? I've been searching the net franticly since this revelation, and I've found little info on the subject. The one thing I came across that was interesting was some health site that said these vitamins play a key roll in a good complexion:

vitamin A,B,C
iron
iodine
protein

I know the iron, iodine and protein are all things that are commonly increased on a low carb diet because you're eating more of the things that contain them. So maybe I just answered my own question, but what I'd really like to know is; can I eat a normal diet and supplement it with the vitamins that I'm not getting enough of and have the same effect?

If someone else has experienced this and can answer my question, I'd certainly appriceate it. I hope this info atleast helps someone find a cure that will work for them.