Girth (tack) Girth (tack) A girth, sometimes called a cinch (Western riding), is a piece of equipment used to keep the saddle in place on a horse or other animal. It passes under the barrel of the equine, usually attached to the saddle on both sides by two or three leather straps called billets. Girths are used on Australian and English saddles, while western saddles and many pack saddles have a cinch, which is fastened to the saddle by a single wide leather strap on each side, called a latigo. Although a girth is often enough to keep a well-fitting saddle in
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