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Pré-Publication, Document De Travail Année : 2021

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

Carla Groenland
  • Fonction : Auteur
Tom Johnston
  • Fonction : Auteur
Andrey Kupavskii
Kitty Meeks
  • Fonction : Auteur
Alex Scott
  • Fonction : Auteur
Jane Tan
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-03236547 , version 1 (26-05-2021)

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Carla Groenland, Tom Johnston, Andrey Kupavskii, Kitty Meeks, Alex Scott, et al.. Reconstructing the degree sequence of a sparse graph from a partial deck. 2021. ⟨hal-03236547⟩
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