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) 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