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

Groenland, C., Johnston, T., Kupavskii, A., Meeks, K. , Scott, A. and Tan, J. (2022) Reconstructing the degree sequence of a sparse graph from a partial deck. Journal of Combinatorial Theory, Series B, 157, pp. 283-293. (doi: 10.1016/j.jctb.2022.07.004)

Abstract

The deck of a graph G is the multiset of cards {G − v : v ∈ V (G)}. Myrvold (1992) showed that the degree sequence of a graph on n ≥ 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/d3) 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Meeks, Dr Kitty
• Authors: Groenland, C., Johnston, T., Kupavskii, A., Meeks, K., Scott, A., and Tan, J.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Journal of Combinatorial Theory, Series B
• Publisher: Elsevier
• ISSN: 0095-8956
• ISSN (Online): 1096-0902
• Published Online: 03 August 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Journal of Combinatorial Theory, Series B 157: 283-293
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
173318		Exploiting realistic graph structure	Kitty Meeks	The Royal Society of Edinburgh (ROYSOCED)	Personal Research Fellows	Computing Science