Horse collar of the Oseberg ship burial). The problem with a breastcollar harness was that the actual shafts of the cart, chariot, or other vehicle are attached to a surcingle around the barrel of the horse. The breastplate primarily kept the surcingle from slipping back, not as the primary pushing object. This results in the horse literally pulling the load, a less efficient use of the animal. The modern breastcollar has traces which transfer the pull directly from the breastcollar, but a horse collar still is more effective for pulling heavy loads. After the breastcollar harness, the next and final evolutionary stage
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