Width varied slightly over the years, but I think most are 1 11/16ths or 1 5/8ths. Other Gibson solid bodies have had narrower necks (the '70's L6S singlecut was around 1 9/16ths, for example).
But when most folks are talking about slim or thin necks, they're talking about depth. Otherwise you'll hear necks referred to as wide or narrow (usually referring to nut width rather than E to E).
I have a custom-built LP (non-Gibson, that is) that has a slightly wider (around 1 3/4" at the nut) neck *and* a thinner neck (17mm at the first fret, tapering to 20.5mm at the 12th).
