Edge Deletion Preserving the Diameter of the Hypercube

Abstract We give upper and lower bounds to the number un− (Qn) of edges that one can remove from a hypercube without altering its diameter, namely: (n − 2)2 n − 1 − ( n ⌊ n 2 ⌋) + 2 ⩽ un − (Q n ) ⩽(n − 2)2 n − 1 + 1 − ⌈ (2 n − 1) (2n − 1) ⌉ .