Researchers from the University of Nottingham in a study allowed women to manipulate the facial colour of computer pictures of men to make them as attractive, dominant or aggressive as possible.
Red colouring in male primates, birds and fish has long been associated with social dominance and mate selection. But it was not known whether this applied to humans, The Independent reported.
Researchers found that as the face gets redder it is increasingly seen as a sign of dominance: the colour is associated with testosterone, health and, in extreme cases, anger.
In the study, they found that increased redness enhanced the appearance of dominance, aggression and attractiveness in men's faces viewed by women.
One theory is that a male face which is red but not too furious-looking is attractive to women because it is interpreted as an indication of good health. A slight increase in redness caused by oxygenated blood perfusion is a marker of fitness.
However, most women are likely to be turned off by too much ruddiness.
"The differences may reflect a trade-off between the benefits to females of choosing a healthy, dominant male and the costs of associating with an aggressive partner," researchers said.
"Red is often a colour of danger. A red face indicates physical or emotional exertion, and may be caused by factors such as intense anger, physical activity or alcohol consumption," Samantha Mann, research fellow and psychologist at the University of Portsmouth, said.
"Perhaps none of these are as appealing to a woman as a simple, healthy glow, but certainly the former two may be associated with dominance or aggression. Conversely, a pale face is more likely to be associated with fear or sickliness. Hence, it figures that a healthy pink is found to be most attractive in a potential mate," Mann said.
"Examples of a very red face that people may see as aggressive might include, in extremis, the Red Skull villain from Marvel comics and film. A dominant but not aggressive face might be Sir Richard Branson or Bill Clinton, and a slightly red attractive face, Brad Pitt," Mann added.