English

Asymptotically Almost Every $2r$-regular Graph has an Internal Partition

Combinatorics 2017-08-17 v2

Abstract

An internal partition of a graph is a partitioning of the vertex set into two parts such that for every vertex, at least half of its neighbors are on its side. We prove that for every positive integer rr, asymptotically almost every 2r2r-regular graph has an internal partition.

Keywords

Cite

@article{arxiv.1708.04162,
  title  = {Asymptotically Almost Every $2r$-regular Graph has an Internal Partition},
  author = {Nathan Linial and Sria Louis},
  journal= {arXiv preprint arXiv:1708.04162},
  year   = {2017}
}

Comments

7 pages

R2 v1 2026-06-22T21:14:07.627Z