Maximal buttonings of trees

摘要

A buttoning of a tree that has vertices v_(1), v_(2), . . , v_(n) is a closed walk that starts at v_(1) and travels along the shortest path in the tree to v_(2), and then along the shortest path to v_(3), and so forth, finishing with the shortest path from v_(n) to v_(1). Inspired by a problem about buttoning a shirt inefficiently, we determine the maximum length of buttonings of trees.