Bitting rig rig." It is the use of additional reins such as the overcheck, or the use of leverage to place the horse's head in a set position that turns a classic surcingle into a bitting rig. Both a bitting rig and a classic surcingle with side reins are intended only to be used while longeing a horse. They are not to be used on a horse that is standing in a stall (though this is a very common type of misuse), nor are they used while riding. However, the surcingle and side reins are used as safety tools in the sport
Girth (graph theory) repeating the Mycielskian construction used to form the Grötzsch graph produces triangle-free graphs of arbitrarily large chromatic number. Paul Erdős was the first to prove the general result, using the probabilistic method. More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a