caterpillar tree

Wiktionary

1. n. graph theory A tree consisting of only a path (the spine or stalk of the tree) and vertices 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. n. botany Catalpa bignonioides; the Southern catalpa tree, a deciduous tree of family Bignoniaceae growing in Southeastern U.S., which is the host plant for the catawba worms, caterpillars that are popular fishing bait.