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.

中文翻译：

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图的大小可重构性

图 $G$ 的牌组由（未标记的）子图 $\{Gv:v\in V(G)\}$ 的多重集给出。子图$Gv$被称为$G$的卡片。Brown 和 Fenner 最近表明，对于 $n\geq29$，可以从缺少 2 张牌的任何一副牌中计算出图 $G$ 的边数。我们表明，对于足够大的 $n$，可以从最多缺少 $\frac1{20}\sqrt{n}$ 卡的任何一副牌中计算边的数量。