Properties of B-Trees

2. Every leaf has the same depth equal to the height of the tree.

3. The number of keys is bounded in terms of the minimum degree t $\geq$ 2.

n(x) $\geq$ t-1 (except root $\geq$ 1)

#children(x) $\geq$ t (except root $\geq$ 0), leaves = 0

n(x) $\leq$ 2t - 1

#children $\leq$ 2t (except leaves which = 0)

If n(x) = 2t - 1 then n is a full node.

For example, if t = 3:

• Root: n(x) = [1..5], #children = [0..6]
• Internal node: n(x) = [2..5], #children = [3..6]
• Leaf: n(x) = [2..5], #children =