I have the following claim:

If a key in a red-black tree has exactly one child (which isn’t null) then he is always red. prove or disprove it.

**My attempt:**

$Disproof.$

we shall represent a counter-example:

This tree satisfies the conditions of being a red-black tree,

since:

- the root is black.
- all leaves are black.
- there isn’t a red key.
- in each path there is the same amount of black keys, in particular, we have three black keys in such paths.

* However*, we have two keys in level-1, which have one child and he is black.

$qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad blacksquare$

Is this disproof right? because perhaps I missed something, and this counter-example doesn’t represent a counter-example. Thanks!