Australian Stock Saddle much deeper seat, higher cantle, and knee pads in the front to create a very secure saddle for riders who ride in rough conditions or spend long hours on a horse. The saddle is kept on with a girth attached to billets under the flaps, similar to those on a dressage saddle. A surcingle passing over the seat of the saddle is also used to provide additional safety. The rear of the saddle is sometimes secured by a crupper. A breastcollar is sometimes added. A saddle blanket or numnah is used under the saddle to absorb sweat and to protect
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