Horses in warfare of today's English saddle. Both the Scythians and Assyrians used pads with added felt attached with a surcingle or girth around the horse's barrel for increased security and comfort. Xenophon mentioned the use of a padded cloth on cavalry mounts as early as the 4th century BC. The saddle with a solid framework, or "tree", provided a bearing surface to protect the horse from the weight of the rider, but was not widespread until the 2nd century AD. However, it made a critical difference, as horses could carry more weight when distributed across a solid saddle tree. A solid tree,
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