Super-free Graphs

Using the definition of \(k\)-free, a known result can be re-stated as follows: If \(G\) is not edge-reconstructible then \(G\) is \(k\)-free, for all even \(k\). To get closer, therefore, to settling the Edge-Reconstruction Conjecture, an investigation is begun into which graphs are, or are not, \(k\)-free (for different values of \(k\), in particular for \(k = 2\)); we also discuss which graphs are \(k\)-free, for all \(k\).