In reply to timO and others: Even on steep rock climbing, a 7.5mm twin rope used as a single will handle any SINGLE climbing fall (even those approaching FF2) with no problem.
The only difference between taking an initial fall on a 7.5mm rope is that you'll fall about twice as far on rope stretch compared to an 11mm one. The big danger is SUBSEQUENT falls where falls that you could take all day on a thick single could very easily result in a much thinner rope braking.
Most people can't afford a new rope every Alpine route so sticking to UIAA/CE approved single ropes ensures that you have enough safety margin to carry on using them after taking moderately large falls on them. But where very big falls are unlikely or impossible, it makes sense to consider much thinner ropes. The obvious cases are glacier travel and mountaineering on slopes less than perhaps 60 degrees.
An 11mm rope has about twice the cross section of a 7.5mm one. However, what we don't know is how 'sharp edge resistance' various with cross-section. I think that there probably aren't many real world cases where an 11mm would hold a 7.5mm cut through. Thicker ropes will be safer but it's worth remembering we don't know how much safer.
We now have 9mm double ropes and 'skinny' 9mm singles. In term of sharp edge performance, I might actually trust the old fashioned double more, since it probably has the thicker sheath. But in the absence of repeatable testing, in any circumstance where I'm worried about very sharp rock I would always want to use double or twin rope technique regardless of other considerations.