The deck of a graph $G$ is given by the multiset of (unlabelled) subgraphs $\{ G-v:v\in V(G)\}$. The subgraphs $G-v$ are referred to as the cards of $G$. Brown and Fenner recently showed that, for $n\geq29$, the number of edges of a graph $G$ can be computed from any deck missing 2 cards. We show that, for sufficiently large $n$, the number of edges can be computed from any deck missing at most $\frac1{ 20}\sqrt{ n}$ cards.
Categories: math.CO