What is "caterpillar tree"

n. 1 (context graph theory English) A tree consisting of only a path (the spine or stalk of the tree) and vertex directly connected to (i.e. one edge away from) that path; a tree whose vertices with a degree of at least 3 are all surrounded by at most two vertices of degree two or greater. 2 (context botany English) (taxlink Catalpa bignonioides species noshow=1); the (vern: southern catalpa), a deciduous tree of family Bignoniaceae growing in Southeastern U.S., which is the host plant for the (vern: catawba worm)s, caterpillars that are popular fishing bait.

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 colorfully write, "A caterpillar is a tree which metamorphoses into a path when its cocoon of endpoints is removed."