Charles Ellicott Commentary 1 Kings 11:12-13

"Notwithstanding in thy days I will not do it, for David thy father`s sake: but I will rend it out of the hand of thy son. Howbeit I will not rend away all the kingdom; but I will give one tribe to thy son, for David my servant`s sake, and for Jerusalem`s sake which I have chosen." — 1 Kings 11:12-13 (ASV)

For David my servant’s sake—that is, evidently, in order to fulfill the promise to David. By the postponement of the chastisement, the blessing promised to his son personally would still be preserved; by retaining the kingdom, though shorn of its splendor and limited to Judah, the larger and more important promise—the continuance of the family of David until 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.