Twelve knights guard the board

What is the fewest knights that together attack every empty square? That minimum is the knight domination number of the board. Knights are short-range and their attack pattern is scattered, so covering the whole board efficiently is delicate, and removing even one knight from a minimal cover leaves a hole.

As with queens, finding a minimal knight cover is a construction, while proving that one fewer cannot do it is the hard direction, argued by showing those knights cannot reach enough squares. Domination numbers measure how efficiently a piece's reach spreads across the board.