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,
Girth (graph theory) coloring must be small and which therefore requires at least colors in any coloring. The odd girth and even girth of a graph are the lengths of a shortest odd cycle and shortest even cycle respectively. The circumference of a graph is the length of the "longest" cycle, rather than the shortest. Thought of as the least length of a non-trivial cycle, the girth admits natural generalisations as the 1-systole or higher systoles in systolic geometry. Girth is the dual concept to edge connectivity, in the sense that the girth of a planar graph is the edge connectivity of its