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 , asymptotically almost every -regular graph has an internal partition.
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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}
}
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7 pages