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arXiv · 2102.08679

Reconstructing the degree sequence of a sparse graph from a partial deck

Carla Groenland·Tom Johnston·Andrey Kupavskii·Kitty Meeks·Alex Scott·Jane Tan
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Abstract

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.

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Carla Groenland, Tom Johnston, Andrey Kupavskii, Kitty Meeks, Alex Scott, Jane Tan. 2021-02-17. Reconstructing the degree sequence of a sparse graph from a partial deck. https://arxiv.org/abs/2102.08679

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