Term for most degenerate tree with two children on every inner node I'm looking for the name of a binary tree which is almost degenerate: at least one child of every interior node in the tree is a leaf.



(Image from Penn State course STAT 557, Data Mining, lesson 10.)
This is a binary tree, when by a binary tree we mean a tree where each vertex has at most 2 children. In other words, you have a tree of maximum degree 3. Also, generally a tree that has a dominating path is a caterpillar.