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) graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is the unique 6-cage, the McGee graph is the unique 7-cage and the Tutte eight cage is the unique 8-cage. There may exist multiple cages for a given girth. For instance there are three nonisomorphic 10-cages, each with 70 vertices: the Balaban 10-cage, the Harries graph and the Harries–Wong graph. For any positive integers and , there exists a graph with girth at least and chromatic number at least ; for instance, the Grötzsch graph is triangle-free and has chromatic number 4, and