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
Matroid girth the use of girth in graph theory, meaning the length of the shortest cycle in a graph: the girth of a graphic matroid is the same as the girth of its underlying graph. The girth of other classes of matroids also corresponds to important combinatorial problems. For instance, the girth of a co-graphic matroid (or the cogirth of a graphic matroid) equals the edge connectivity of the underlying graph, the number of edges in a minimum cut of the graph. The girth of a transversal matroid gives the cardinality of a minimum Hall set in a bipartite graph: this is