The deck of a graph G is the multiset of cards $\{G-v:v\in V(G)\}$. Myrvold (1992) showed that the degree sequence of a graph on $n\ge 7$ vertices can be reconstructed from any deck missing one card. We prove that the degree sequence of a graph with average degree d can be reconstructed from any deck missing $O(n/d^3)$ cards. In particular, in the case of graphs that can be embedded on a fixed surface (e.g. planar graphs), the degree sequence can be reconstructed even when a linear number of the cards are missing.

中文翻译：

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从部分甲板重建稀疏图的度数序列

图G的牌组是多组牌$\{G-v：v\in 五(G)\}$. Myrvold (1992) 表明，图的度数序列$n\ge 7$顶点可以从任何缺少一张牌的牌组中重建。我们证明了一个平均度数为d的图的度数序列可以从任何缺失的甲板上重建$○(n/d^3)$牌。特别是，在可以嵌入固定表面的图（例如平面图）的情况下，即使丢失了线性数量的卡片，也可以重建度数序列。