Kart Tires are one of the reasons that karts go so fast around tracks. With the karts being small, the tires are a greater percentage of contact to the ground than in a bigger car. This helps handling tremendously. A popular brand in America are Dunlop Kart Tires.
All of the karting tires for different types of karts are all around the same size. They are mounted on six inch or five inch wheels and between the sizes of 10x3.60-5 to 11.5x8.00-6. The first number is the diameter, the second number is for the width, and the last number is the diameter of the wheel it's mounted on. They are measured in inches.
An example of a tire company that only makes tires on six inch wheels are Firestone Kart Tires. Their close partner, Bridgestone Kart Tires, makes most of their tires to fit 5 inch wheels.
When you hear compound, they are talking about the softness/hardness of the tire. Things called durometers can measure this by just touching the tire with it. It gives a numbered reading on how hard or soft the tire is.
Generally a soft tire will give you more grip and won't last as long and a hard tire will give you less grip and last longer. You have to judge what you need at each racetrack. It is not uncommon for you to change tires between races multiple times in one day. As conditions change, you might need a different size tire or a softer or harder tire.
Dirt tires are sometimes softer tires than asphalt, because you need more grip, but with how dirt kart tracks are, sometimes they end up using the same hardness of tires. Maxxis kart tires make a great dirt tire for America. The left rear tire of a kart will usually be pretty hard and small because you don't want that tire to do much in the turns - it would only slow you down.
Even though these are banned, they may continue to be used in between races off-track.
There is no way for any organization to test the tire to see if tire prep has been used off the track.
As these were introduced they got really popular. They are basically solvents that change the rubber on the tire. Almost always it was used to make it softer. These are banned in most racing organizations and will probably not be allowed at many places soon. It adds an unwanted level to preparing a tire for a race, and can be damaging to the rubber. Vega Tires offer a tire that is advertised to not need prep at all and still be as successful.
Slick tires and Rain tires are the most common types. Rain kart tyres(not a typo - This is the way it's written in a lot of places) are softer and have special cut grooves or patterns in them to drain water away from the tire and make it handle better in wet conditions. Slick tires are not grooved and are the most common for dry conditions. Most dirt karts use slick tires that are soft, but some tracks or certain types of karts they have to use grooved tires to handle through turns.
The brands on this page are the major companies. There isn't much difference between kart racing tires, but they all have their minor differences that make up what they are.