Is a tree with all black nodes a red black tree?

A red-black tree is simply a binary-tree representation of a 2-3-4 tree . Any red node in a red-black tree corresponds to a piece of its parent node in the analagous 2-3-4 tree. For example.

It is possible to have a proper red-black tree that has all black nodes. Trivially, a RBTree with only one node, or with the only leaf nodes being direct children of the root, will be all back nodes.

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