Internal Partitions of Regular Graphs

Amir Ban, Nati Linial

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


An internal partition of an n-vertex graph (Formula presented.) is a partition of V such that every vertex has at least as many neighbors in its own part as in the other part. It has been conjectured that every d-regular graph with (Formula presented.) vertices has an internal partition. Here we prove this for (Formula presented.). The case (Formula presented.) is of particular interest and leads to interesting new open problems on cubic graphs. We also provide new lower bounds on (Formula presented.) and find new families of graphs with no internal partitions. Weighted versions of these problems are considered as well.

Original languageAmerican English
Pages (from-to)5-18
Number of pages14
JournalJournal of Graph Theory
Issue number1
StatePublished - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© 2015 Wiley Periodicals, Inc.


  • cubic
  • external
  • internal
  • partition
  • regular


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