1 Kings 11:12,13 - Ellicott's Commentary On The Whole Bible

For David my servant’s sake — that is, evidently, in order to fulfil the promise to David. By the postponement of the chastisement, the blessing promised to his son personally would be still preserved; by the retaining of the kingdom, though shorn of its splendour, and limited to Judah, the larger and more important promise, the continuance of the family of David till the coming of the Messiah, would be fulfilled. The “one tribe” is, of course, Judah, with which Benjamin was indissolubly united by the very position of the capital on its frontier. This is curiously indicated in 1 Kings 11:31-32, where “ten tribes” are given to Jeroboam, and the remainder out of the twelve is still called “one tribe.”