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

Nathan Linial; Sria Louis

doi:10.1007/s00373-019-02116-0

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

Nathan Linial, Sria Louis^*

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 language	English
Pages (from-to)	41-50
Number of pages	10
Journal	Graphs and Combinatorics
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s00373-019-02116-0
State	Published - 1 Jan 2020

Bibliographical note

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

Keywords

Asymptotic
Graph partitions
Internal partition
Optimization
Satisfactory partition
Vertex degree

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KW - Optimization

KW - Satisfactory partition

KW - Vertex degree

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

Abstract

Bibliographical note

Keywords

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