How can a node with one child be removed from a tree?

When removing a node that has one child from a tree, promoting the child is the appropriate action. This process involves updating the parent of the node to point directly to its only child, thereby effectively removing the node while still preserving the tree's structure.

Promoting the child means that the single child of the node takes the place of the node being deleted. This action maintains the binary search tree properties if the tree is organized as such, as the promotion of the child maintains all necessary ordering. The parent now references the child directly, allowing it to continue functioning within the tree without introducing any inconsistencies.

The other methods of removal, such as deleting both nodes or replacing the node with a leaf, do not accurately represent valid or efficient techniques in maintaining tree structure. Relinking a parent directly to a grandchild is only applicable in scenarios where a node has two children and not one, as it would require careful consideration of the subtree to ensure that the binary search tree properties are preserved. Thus, promoting the child accurately addresses the removal process when a node has only one child.