Bronc riding toward the rigging handle, spurring at each jump in rhythm with the motion of the horse. Bareback bronc riding began to develop as a professional rodeo sporting event around 1900. The riding equipment used during that era varied. In some cases, the rider simply held onto the horse's mane, called a mane-hold. Others held a loose or twisted rope tied around the horse's girth, and other methods involved using multiple handhold leather riggings based on a surcingle. In the early 1920s, when the old rodeo rules allowing two handed riding were being phased out and replaced with the newer rule
Girth (graph theory) repeating the Mycielskian construction used to form the Grötzsch graph produces triangle-free graphs of arbitrarily large chromatic number. Paul Erdős was the first to prove the general result, using the probabilistic method. More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a