YDKs seem to be "WetBridgestone YDK (front 10 x 3.6 x 5, rear 11 x 6.0 x 5)"
'3.6' indicates the tyre is 3.6 wide but this ia a) an approximation and b) doesn't seem related to any particular point on the tyre, possibly because the tyre width can be affected by the way it is stored and so on.
This suggests a rim anywhere between 3.6 and 5 inches (91 to 125mm) can be used with the tyre.
see (http://www.russellkarting.com/range.htm) with an average choice of 4 inch (100 mm)
However there are all sorts of reasons to use different widths depending on the tyre construction, your weight and the conditions and the availabilty of rims in that width.
Also, having been inflated and driven, the tyres may stretch so that they fit better.
You can completely alter the handling characteristics of the tyre by using a wider rim which tends to brace the tread, while using a narrower rim tends to cause the tyre to 'sway' more (because the walls are being made to flex).
Theoretically working the walls makes the tyre hotter, but overworking the walls makes the tyre handling more erratic. This being the first set of wets you have bought suggests that you are relatively new in the sport The right choice of rims will depend on you, the kart weight, your driving, the wetness of the track and all sorts of other variables.
While 115mm are within the limits for the tyre, I would have thought that narrower rims would be better for a relatively inexperienced driver. One of the problems with wet driving is simply to get the tyres hot enough, which means getting a lot of energy into the tread. Many novices find that driving fast enough in the wet to get the grip that allows you to have confidence to 'lean on' the tyre is difficult and scary.
As so often with karting, there is no 'right' answer and you will have to experiment. Also, what is right one day may not be right in different conditions, a warm summer track recently showered on will be different from a cold-soaked winter track after a night of freezing, heavy rain. On the other hand a prokart driver may come along and say that 115mm rims are just what you need because the tyres are so soft they need to move very little on the rims.
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