Seems to me that the hose is one of those aluminum hoses with a plastic elbow that goes in the front of the air cleaner intake. I had mine off, but had to put it back on. As well, my emissions hoses and sensors were half missing or blocked off. Some of the sensors are gone too. With the emission hoses and sensors not connected, the gate on the air cleaner doesn't seem to know when to let the warm air into the intake.This gate controls the hot air going into the carb from the exhaust. I rigged it open for the winter because it stayed closed only allowing cold air in the the carb. The carb would get too cold of air and the engine would stall. Right now, I have a lack of power and undesirable gas mileage, but she starts right up, and keeps running even down to 5 degrees.
I got my hands on all the emissions stuff but haven't had the time or weather conditions to put them on. I will definitely do so first chance I get. Hopefully all will be back to normal at that point.
You can get a brand new hose with the elbow included (I think) from suzuki for about $26.00. Or you can also try Hawk for a new or used one. Auto parts stores only seem to have sae sizes. This hose is I think 55 mm diameter by 3 feet long. You have to have the plastic elbow or the air intake side because it transitions the aluminum hose to the intake tube.
Hope that helps.
-Adam