Surcingle Surcingle A surcingle is a strap made of leather or leather-like synthetic materials such as nylon or neoprene, sometimes with elastic, that fastens around the horse's girth. A surcingle may be used for ground training, some types of in-hand exhibition, and over a saddle or horse pack to stabilize the rider's weight. It also is a primary component of a horse harness. A basic surcingle is unpadded, attaches around the horse by means of buckles or rings, and has no other hardware. A training surcingle, sometimes called a "roller," has many extra rings attached, running from the ribcage up to
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