A spanning subgraph H of a graph G is a 2-detour subgraph of G if for each x, y V (G), dH (x, y) dG(x, y) + 2. We prove a conjecture of Erdos, Hamburger, Pippert, and Weakley by showing that for some positive constant c and every n, each 2-detour subgraph of the n-dimensional hypercube Qn has at least c log2 n
József Balogh, Alexandr V. Kostochka