Carbohydrates have been linked to this skin condition, so cutting down on them may help. And the drop in insulin that a ketogenic diet can trigger may also help stop acne breakouts. (Insulin can cause your body to make other hormones that bring on outbreaks.) Still, more research is needed to determine exactly how much effect, if any, the diet actually has on acne.
This is a new area, but the research that has come out since this article is also positive, and promising. One example: In this June 2018 study of 23 people with obesity, 12 weeks of 8-hour time-restricted feeding resulted a 2.6% decrease in body weight and a 7 point decrease in systolic blood pressure, which was significant when compared to controls: https://www.ncbi.nlm.nih.gov/pubmed/29951594
Conklin's fasting therapy was adopted by neurologists in mainstream practice. In 1916, a Dr McMurray wrote to the New York Medical Journal claiming to have successfully treated epilepsy patients with a fast, followed by a starch- and sugar-free diet, since 1912. In 1921, prominent endocrinologist Henry Rawle Geyelin reported his experiences to the American Medical Association convention. He had seen Conklin's success first-hand and had attempted to reproduce the results in 36 of his own patients. He achieved similar results despite only having studied the patients for a short time. Further studies in the 1920s indicated that seizures generally returned after the fast. Charles P. Howland, the parent of one of Conklin's successful patients and a wealthy New York corporate lawyer, gave his brother John Elias Howland a gift of $5,000 to study "the ketosis of starvation". As professor of paediatrics at Johns Hopkins Hospital, John E. Howland used the money to fund research undertaken by neurologist Stanley Cobb and his assistant William G. Lennox. https://weightlossscience.tumblr.com/