caterpillar tree
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In graph theory, a caterpillar or caterpillar tree is a tree in which all the vertices are within distance 1 of a central path.
The central path can be viewed as the caterpillar‘s "body" and the other vertices can be viewed as its "feet".
A tree is a caterpillar if and only if it becomes a path when all of its leaves are removed. Here a leaf means a vertex of degree one in the original tree.
It can be proved that a diameter of a caterpillar is always its body.
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