Longeing piece of twine or rope, though for a very skittish young horse they also can be thrown up over the top of the saddle and tied down in that fashion. A surcingle or roller is a padded band that straps around the horse's girth area, and has rings around on its side for side reins, or long reins or other training equipment, such as an overcheck. It may also be used on a young horse to get it used to girth pressure. It may be used with or without an English saddle underneath. Side reins are usually used for more
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