Caterpillar-tree meaning

(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.
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(botany) Catalpa bignonioides; the southern catalpa, 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.
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