Caterpillar tree

In graph theory, a caterpillar or caterpillar tree is a tree in which all the vertices are within distance 1 of a central path.

Caterpillars were first studied in a series of papers by Harary and Schwenk. The name was suggested by A. Hobbs. As Harary & Schwenk (1973) colorfully write, "A caterpillar is a tree which metamorphoses into a path when its cocoon of endpoints is removed."