稀疏图的度序列的部分deck重构
Reconstructing the degree sequence of a sparse graph from a partial deck
摘要：
图$G$的卡片组是卡片的多重集合$\{G-v:v\in V(G)\}$。Myrvold（1992）证明了一个图在$n\geq7$顶点上的度序列可以从任何缺少一张牌的牌组中重建出来。我们证明了具有平均度$d$的图的度序列可以从任何缺失$O(n/d^3)$卡片的卡片组中重构。特别地，在可以嵌入在固定表面上的图（例如，可平面图）的情况下，即使当线性数量的卡缺失时，也可以重建度序列。
英文摘要：
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 $n\geq7$ vertices can be reconstructed from any deck missing one card. We prove that the degree sequence of a graph with average degree $d$ can 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
