Girth (tack) sensitive horses to protect the barrel of the horse, and some styles of girth come with attached or removable sheepskin liners that perform the same function. A dressage girth, or Lonsdale girth, is shorter than the usual girths used on other saddles. This is because the dressage saddle has longer billets, to keep the buckles out from under the rider's leg, and so a shorter girth may be used. Dressage girths can be made of all the materials, and in all the styles, mentioned before, and also can be made entirely of very strong elastic. An overgirth or surcingle is
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