Super-free Graphs

Abstract

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 $k$.