2 Samuel 2:4

And the men of Judah came, and there they anointed David king over the house of Judah. And they told David, saying, That the men of Jabesh-gilead were they that buried Saul.

The men of Judah came to Hebron and there anointed David as king over the house of Judah. His anointing at that time made him king of Judah alone. His authority was therefore limited to that one tribe. He made no attempt to bring the other tribes under his rule by force.