Surcingle longe lines, requires the use of a surcingle to thread the longe lines through the rings. Compared to a saddle, a surcingle allows more precise adjustment of side reins due to the placement of additional rings. While a saddle only provides one height to attach the rings (the girth buckles), and can be uneven or at the wrong position, a training surcingle places rings at more appropriate locations for ground work. Many surcingle designs allow the side reins to be attached at several different heights along the sides of the horse. When used without a saddle, a surcingle sits just
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