Let G be a graph with vertex degree sequence d1 ≤ d2 ≤ … ≤ dp It is shown that if di + dp–i+1 ≥ p for some i, then G is uniquely reconstructable from its collection of maximal (edge deleted) subgraphs. This generalizes considerably a result of Lovász. As a corollary, it is shown that Chvátal's existence condition for hamiltonian cycles implies edge reconstructability as well.