Asymptotically Almost Every 2r-Regular Graph Has an Internal Partition

Nathan Linial, Sria Louis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


An internal partition of a graph G= (V, E) is a partitioning of V into two parts such that every vertex has at least a half of its neighbors on its own side. We prove that for every positive integer r, asymptotically almost every 2r-regular graph has an internal partition. Whereas previous results in this area apply only to a small fraction of all 2r-regular graphs, ours applies to almost all of them.

Original languageAmerican English
Pages (from-to)41-50
Number of pages10
JournalGraphs and Combinatorics
Issue number1
StatePublished - 1 Jan 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer Japan KK, part of Springer Nature.


  • Asymptotic
  • Graph partitions
  • Internal partition
  • Optimization
  • Satisfactory partition
  • Vertex degree


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